-3x(x+4)=0

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

-3x(x+4)=0

We multiply parentheses

-3x^2-12x=0

a = -3; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·(-3)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*-3}=\frac{0}{-6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*-3}=\frac{24}{-6}
=-4
$