-4x(x+8)=32

Solution for -4x(x+8)=32 equation:

-4x(x+8)=32

We move all terms to the left:

-4x(x+8)-(32)=0

We multiply parentheses

-4x^2-32x-32=0

a = -4; b = -32; c = -32;
Δ = b2-4ac
Δ = -322-4·(-4)·(-32)
Δ = 512
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:

$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-16\sqrt{2}}{2*-4}=\frac{32-16\sqrt{2}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+16\sqrt{2}}{2*-4}=\frac{32+16\sqrt{2}}{-8}
$