Where did I make my mistake?
x = b - a
x(b – a) = (b – a)(b – a)
bx – ax = b^2 – 2ab + a^2

bx – ax – bx + ab – a^2 = b^2 – 2ab + a^2 – bx + ab – a^2
bx – bx – ax + ab – a^2 = –bx + b^2 – 2ab + ab + a^2 – a^2

–ax + ab – a^2 = –bx + b^2 – ab
a(–x + b – a) = b(–x + b – a)
a = b

This is one of those "problems" where you "prove" that everything is equal to everything else. Usually the answer comes out "2=1" or something like that.

If x=(b-a) then -x+b-a = 0 and in your last step you divided both sides by zero. This is an undefined operation so the result is undefined.