(8x-7)(-9x+9)-(8x-7)(6x+7)=0

Solution for (8x-7)(-9x+9)-(8x-7)(6x+7)=0 equation:

(8x-7)(-9x+9)-(8x-7)(6x+7)=0

We multiply parentheses ..

(-72x^2+72x+63x-63)-(8x-7)(6x+7)=0

We get rid of parentheses

-72x^2+72x+63x-(8x-7)(6x+7)-63=0

We multiply parentheses ..

-72x^2-(+48x^2+56x-42x-49)+72x+63x-63=0

We add all the numbers together, and all the variables

-72x^2-(+48x^2+56x-42x-49)+135x-63=0

We get rid of parentheses

-72x^2-48x^2-56x+42x+135x+49-63=0

We add all the numbers together, and all the variables

-120x^2+121x-14=0

a = -120; b = 121; c = -14;
Δ = b2-4ac
Δ = 1212-4·(-120)·(-14)
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{-(121)-89}{2*-120}=\frac{-210}{-240}
=7/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(121)+89}{2*-120}=\frac{-32}{-240}
=2/15
$