-2x(x+4)=6

Solution for -2x(x+4)=6 equation:

-2x(x+4)=6

We move all terms to the left:

-2x(x+4)-(6)=0

We multiply parentheses

-2x^2-8x-6=0

a = -2; b = -8; c = -6;
Δ = b2-4ac
Δ = -82-4·(-2)·(-6)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4}{2*-2}=\frac{4}{-4}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4}{2*-2}=\frac{12}{-4}
=-3
$