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

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

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

We multiply parentheses

9x^2-72x-2x-16=0

We add all the numbers together, and all the variables

9x^2-74x-16=0

a = 9; b = -74; c = -16;
Δ = b2-4ac
Δ = -742-4·9·(-16)
Δ = 6052
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6052}=\sqrt{4*1513}=\sqrt{4}*\sqrt{1513}=2\sqrt{1513}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-74)-2\sqrt{1513}}{2*9}=\frac{74-2\sqrt{1513}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-74)+2\sqrt{1513}}{2*9}=\frac{74+2\sqrt{1513}}{18}
$