-4x(2x-4)-2x-2=-36

Solution for -4x(2x-4)-2x-2=-36 equation:

-4x(2x-4)-2x-2=-36

We move all terms to the left:

-4x(2x-4)-2x-2-(-36)=0

We add all the numbers together, and all the variables

-2x-4x(2x-4)+34=0

We multiply parentheses

-8x^2-2x+16x+34=0

We add all the numbers together, and all the variables

-8x^2+14x+34=0

a = -8; b = 14; c = +34;
Δ = b2-4ac
Δ = 142-4·(-8)·34
Δ = 1284
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:

$\sqrt{\Delta}=\sqrt{1284}=\sqrt{4*321}=\sqrt{4}*\sqrt{321}=2\sqrt{321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{321}}{2*-8}=\frac{-14-2\sqrt{321}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{321}}{2*-8}=\frac{-14+2\sqrt{321}}{-16}
$