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HTML Form Validation - Check for Specific Characters

I'm using the Html5 pattern to validate my inputs on forms. I need to make sure an input has the following rules:
A maximum and minimum of 8 characters
The first 3 must be the specific letters wrx (lowercase)
The last 5 must be numbers.
Eg. wrx12345
Can I even do this with pattern or do I need to use JavaScript?

I believe the regex pattern you are looking for is /^wrx[0-9]{5}$/. A visual representation of this here:
And implemented in html:
<input name="example" pattern="^wrx[0-9]{5}$">

You can use regex in Javascript with this regex:
"/[wrz][\d]{5}/g".
To test the minimum = maximum length = 8, you can just test it in javascript.
If the length egual 8, use the regex
Else, show error
I think this could work

You don't need Javascript to do this.
The pattern attribute uses regular expressions so you can use something like this: ^wrx[0-9]{5}$
The ^ and $ indicates the start and end of the string. Then 'wrx' has to be matched exactly and [0-9]{5} looks for 5 number bewteen 0-9.
You can use something like RegExr to test your patterns.

Why does this regular expression won't work properly?

I'm in the need to check wether some input is strictly as this one:
PEOPLE-123456 or PERSON-12345376 (it can be any combination of numbers)
The number of numbers following the - doesn't matter. It can be from 0 to N numbers.
I've come up with the following expression:
/(PEOPLE-)|(PERSON-)?=^[0-9]+$/
The problem is, this will work even if the characters after the -are not numbers.
PEOPLE-123131 yields true
PERSON-123242 yields true
PERSON-23123.341 yields true
PEOPLE-.2341231 yields false
What am I doing wrong with it? I don't see any problems with the expression itself, maybe I am to noob to see it.

Try this:
^(PERSON|PEOPLE)-[0-9]{1,}$
This ensures the beginnings starts with exactly wither PERSON or PEOPLE, followed by - and ends with at least one number.

You need to put the grouping parentheses around both alternatives:
/^(PEOPLE|PERSON)-\d+$/
And you shouldn't mark it optional with ?. I have no idea why you put = and ^ after that part.
And if you want to allow decimal points in the number, use [0-9.] instead of \d.

This should work if numbers are optional. Otherwise at least 1 number is required replace * with +.
/^(PEOPLE|PERSON)-\d*$/

JavaScript: How to get specific text in a string using RegEx

I tummbled into this RegEx and I googled it. A lot. But unfortunately didn't quite understand how RegEx works...
So to make this quick since only a tiny winny part of my work requires it so I will be needing you guys. again :))
So here it goes...
All I want is to retrieve a specific string with a format of 0000x0000. For example:
Input:NameName975x945NameName
Output:
975x945
Must also consider string like this:
NameNameName9751x9451NameNameName
(the integer and string are longer...)

Use regex in String.prototype.match() to get specific part of string.
str.match(/\d+x\d+/)[0]
var str = "NameName975x945NameName";
var match = str.match(/\d+x\d+/)[0];
console.log(match)

We need a bit more detail, but I'll go in order:
Assuming there can be any number of digits before and after the x, and these can be of different lengths:
[\d]+x[\d]+
Assuming the number of digits before the x needs to be equal to the number of digits after the x (as in your example) and this number is finite (and small enough so that your regex isn't obscenely long):
[\d]{1}x[\d]{1}|[\d]{2}x[\d]{2}|[\d]{3}x[\d]{3} (and so on)
Check out this related answer for more details on handling this as the length of the number gets longer.
Then you can use String.prototype.match() with your regex to grab the matches within your string.

Use Regex in JS to find a particular patten in a particular spot in a string

I'm not particularly strong with Regular Expressions. Basically, I have the following string:
Showing 1-20 of 748 results.
I want to extract the "748", convert it to a number, and use it for comparisons. As expected, "Showing", "of", and "results" are not expected to change, but the numbers could. I have a couple of solutions in mind. The first is using lookbehinds, but I do not believe JS supports them. The second is doing a more blunt approach, maybe finding all the numbers in the string using match() and taking the element at the third index in the returned array (which should be "748").
Any thoughts on the best way to do this?

I would use the regex:
Showing \d+-\d+ of (\d+) results\.
where \d+ in each case means to match 1 or more digits. The parentheses around the number you wanted to find is called a capture group.
So if the search string was in str, the resulting JavaScript might look like:
var resultsRe = /Showing \d+-\d+ of (\d+) results\./;
var numResults = resultsRe.exec(str);
console.log("There are " + numResults + " results.");

For a simple approach you could do the following:
(\d+)\sresults
All it does is capture the integer directly before the word results.

negative number in parentheses using javascript

I use match to split a mathematics expression into separated strings and save them in an array.
var STRING = ST.match(/\d*\.\d+|\d+|[()/*+-]/g);
but this method separate everything including negative numbers which are inside parentheses.
For example (-2+4) does not give me -2, instead it saves - in one index of STRING array and 2 in the next index.
Is there anyway use match and save negative numbers which are in the parentheses?
This is what I want:
(-2+4):
STRING[0] give me (
STRING[1] give me -2
STRING[2] give me +
STRING[3] give me 4
STRING[4] give me )
and if there is no negative number work as normal:
(2+4):
STRING[0] give me (
STRING[1] give me 2
STRING[2] give me +
STRING[3] give me 4
STRING[4] give me )

I don't think it's possible to parse complex cases like "(-2+4*-(3.5--8))" with just a regex especially given we don't have negative look behind in javascript.
A solution would be to postprocess your match array by merging signs when they're between a separator and an unsigned expression.
In my opinion a regex is useful here, but only for the primary tokenization. Most of the work will be ahead of you as you'll build the binary expression tree (or any other formal representation you choose).

Unfortunately, if what you're trying to do is parsing a mathematical expression, regexps can not be used.
RegExps can be used in languages that are describable by Regular Grammars and arithmetical expressions can not, they are described by a Context Free Grammar (CFG). If you want to parse, and perhaps interpret the result, you'll certainly need some stacked state machine.
You can look at something like this well known algorithm.
Hope this helps.

You can add an optional sign to the numbers, that would work with your example:
var STRING = ST.match(/-?\d*\.\d+|-?\d+|[()/*+-]/g);
However, that will also turn a minus operator into a sign. The expression (4-2) would give you { "(", "4", "-2", ")" }.
Also, it will happily "parse" an expression like +---((((*** without complaining. If you want a result that makes sense, you should parse it for real, not just split it with a regular expression.

I think you have some mistake in your RegExp try this, it works for me:
var STRING = ST.match(/(\d*)(\.)(\d+)|(\d+)|[()\/*+-]/g);