-4x(x+6)=8

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

-4x(x+6)=8

We move all terms to the left:

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

We multiply parentheses

-4x^2-24x-8=0

a = -4; b = -24; c = -8;
Δ = b2-4ac
Δ = -242-4·(-4)·(-8)
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{7}}{2*-4}=\frac{24-8\sqrt{7}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{7}}{2*-4}=\frac{24+8\sqrt{7}}{-8}
$