(a - b)^2 x^2 - 4abx - (a-b)^2
solve for x by factorisation method.
The problem is an old one. You have not copied it correctly. It should be
then it can be factored.
In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.