12-6x+4-8x-2x(x-8)=0

Solution for 12-6x+4-8x-2x(x-8)=0 equation:

12-6x+4-8x-2x(x-8)=0

We add all the numbers together, and all the variables

-14x-2x(x-8)+16=0

We multiply parentheses

-2x^2-14x+16x+16=0

We add all the numbers together, and all the variables

-2x^2+2x+16=0

a = -2; b = 2; c = +16;
Δ = b2-4ac
Δ = 22-4·(-2)·16
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{33}}{2*-2}=\frac{-2-2\sqrt{33}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{33}}{2*-2}=\frac{-2+2\sqrt{33}}{-4}
$