I'm trying to solve this equation for x.

.6 = x / x + 20

I can tell that X=30, but how do I prove that mathematically? We can't just plug in numbers, we have to show where we got them from.

you probably mean

.6 = x /(x + 20)
6/10 = x/(x+20)
cross-multiply
10x = 6x + 120
4x = 120
x = 30