(9x-5)(7x+6)=0

Solution for (9x-5)(7x+6)=0 equation:

(9x-5)(7x+6)=0

We multiply parentheses ..

(+63x^2+54x-35x-30)=0

We get rid of parentheses

63x^2+54x-35x-30=0

We add all the numbers together, and all the variables

63x^2+19x-30=0

a = 63; b = 19; c = -30;
Δ = b2-4ac
Δ = 192-4·63·(-30)
Δ = 7921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7921}=89$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-89}{2*63}=\frac{-108}{126}
=-6/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+89}{2*63}=\frac{70}{126}
=5/9
$