-4x(x+5)=-8

Solution for -4x(x+5)=-8 equation:

-4x(x+5)=-8

We move all terms to the left:

-4x(x+5)-(-8)=0

We add all the numbers together, and all the variables

-4x(x+5)+8=0

We multiply parentheses

-4x^2-20x+8=0

a = -4; b = -20; c = +8;
Δ = b2-4ac
Δ = -202-4·(-4)·8
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{33}}{2*-4}=\frac{20-4\sqrt{33}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{33}}{2*-4}=\frac{20+4\sqrt{33}}{-8}
$