Is it possible to create custom operators in JavaScript?

No. You can't do that in JS.

The closest you can have IMO is to implement your own object which has a chainable interface, aka "fluent" syntax. That way you can operate as if you were speaking out in sequence.

var eq = new YourEquationObject();

// Then operate like 1 - 2 * 3
eq.add(1).sub(2).mul(3);

Details are up to you though. Just giving out an idea.

No. JavaScript does not support operator overloading . but you can make a class method for doing this

var mathClass = function(value){
   this.value = value;
}

mathClass.prototype.toLaw = function(){
   return 2 * this.value;
}

var y = new mathClass(2)
2 + y.toLaw(); //2 + 2 * y

You can add pseudo-operators via methods on Number.prototype:

Object.defineProperty(Number.prototype, 'myOp', {
    value: function(that) {
        return this + 2 * that;
    }
});

Then all of this syntax will work

alert( (2).myOp(2) )
alert( 2 .myOp(2) )
alert( 2..myOp(2) )
alert( 2.0.myOp(2) )

2.myOp(2) does not work because the period is treated as a decimal point

The slightly longer then the short one is that Yes you can, but its a bit more involved then what you did in Math class

To extend the language with new constructs you can use a transformer like http://esprima.org/ or any of the others. You need to define your syntax, write the parser to parse your statement and finally add the actual code to do the math parts. When these parts is in place you have made a new language that works just as javascript but with the added support of the ∘ operator.

Its really not that hard to add new syntax, here is facebooks example how they add => arrow function syntax

https://github.com/facebook/jstransform/blob/master/visitors/es6-arrow-function-visitors.js

Read the comments below the answer.

Apparently you can't. Here is something close :

function exec(input) {
    return Function(
        'return ' + input.replace(/∘( *[\d.]+)/g, '+ 2 * $1') + ';'
    )();
}

exec('2 ∘ 2'); // 6