0=12x^2+6x

Solution for 0=12x^2+6x equation:

0=12x^2+6x

We move all terms to the left:

0-(12x^2+6x)=0

We add all the numbers together, and all the variables

-(12x^2+6x)=0

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