(9x+8)(-7x+9)+(9x+8)(2x-4)=0

Solution for (9x+8)(-7x+9)+(9x+8)(2x-4)=0 equation:

(9x+8)(-7x+9)+(9x+8)(2x-4)=0

We multiply parentheses ..

(-63x^2+81x-56x+72)+(9x+8)(2x-4)=0

We get rid of parentheses

-63x^2+81x-56x+(9x+8)(2x-4)+72=0

We multiply parentheses ..

-63x^2+(+18x^2-36x+16x-32)+81x-56x+72=0

We add all the numbers together, and all the variables

-63x^2+(+18x^2-36x+16x-32)+25x+72=0

We get rid of parentheses

-63x^2+18x^2-36x+16x+25x-32+72=0

We add all the numbers together, and all the variables

-45x^2+5x+40=0

a = -45; b = 5; c = +40;
Δ = b2-4ac
Δ = 52-4·(-45)·40
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-85}{2*-45}=\frac{-90}{-90}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+85}{2*-45}=\frac{80}{-90}
=-8/9
$