24=6x^2+6x-12

Solution for 24=6x^2+6x-12 equation:

24=6x^2+6x-12

We move all terms to the left:

24-(6x^2+6x-12)=0

We get rid of parentheses

-6x^2-6x+12+24=0

We add all the numbers together, and all the variables

-6x^2-6x+36=0

a = -6; b = -6; c = +36;
Δ = b2-4ac
Δ = -62-4·(-6)·36
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-30}{2*-6}=\frac{-24}{-12}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+30}{2*-6}=\frac{36}{-12}
=-3
$