-4x(3x+8)=0

Solution for -4x(3x+8)=0 equation:

-4x(3x+8)=0

We multiply parentheses

-12x^2-32x=0

a = -12; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·(-12)·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*-12}=\frac{0}{-24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*-12}=\frac{64}{-24}
=-2+2/3
$