solve

p2x2+(p2-q2)x-q2=0

p²x²+(p²-q²)x-q²=0

p2x2 + p2x - q2x - q2 = 0

p2x ( x + 1 ) - q2 ( x + 1 ) = 0

( x + 1 ) = 0 or ( p2x - q 2 ) = 0

therefore x = -1 or x = q2 / p2