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

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

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

We multiply parentheses

9x^2+72x-4x-32=0

We add all the numbers together, and all the variables

9x^2+68x-32=0

a = 9; b = 68; c = -32;
Δ = b2-4ac
Δ = 682-4·9·(-32)
Δ = 5776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5776}=76$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-76}{2*9}=\frac{-144}{18}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+76}{2*9}=\frac{8}{18}
=4/9
$