Solve the following quadric equation for x :

4x² + 4bx – (a² – b²) = 0

Equation can be re - written as

4x² + 4bx + (b² – a²) = 0

4x² + 2(b - a)x + 2(b + a)x + (b - a)(b + a) = 0 [ as x² - y² = (x + y) (x - y) ]

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

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