-2x(4x+2)=0

Solution for -2x(4x+2)=0 equation:

-2x(4x+2)=0

We multiply parentheses

-8x^2-4x=0

a = -8; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-8)·0
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{-(-4)-4}{2*-8}=\frac{0}{-16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-8}=\frac{8}{-16}
=-1/2
$