-2x(x+8)=12

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

-2x(x+8)=12

We move all terms to the left:

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

We multiply parentheses

-2x^2-16x-12=0

a = -2; b = -16; c = -12;
Δ = b2-4ac
Δ = -162-4·(-2)·(-12)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{10}}{2*-2}=\frac{16-4\sqrt{10}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{10}}{2*-2}=\frac{16+4\sqrt{10}}{-4}
$