x(12x+6)=0

Solution for x(12x+6)=0 equation:

x(12x+6)=0

We multiply parentheses

12x^2+6x=0

a = 12; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·12·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*12}=\frac{-12}{24}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*12}=\frac{0}{24}
=0
$