Using splitting middle term, the middle term of the general equation is divided in two such values that:

Product = a.c

For the given equation

= =

And either of their sum or difference = b

=

Thus the two terms are

Sum =

=

=

Product = using

= =

x[x-(2a + b)]-(2a-b)[x-(2a + b)] = 0

[x-(2a-b)][x-(2a + b)] = 0

[x-(2a-b)] = 0 or [x-(2a + b)] = 0

x = (2a-b) or x = (2a + b)

Hence roots of equation are x = (2a - b) or x = (2a + b)