(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.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.