2x+12=3x^2-108

Solution for 2x+12=3x^2-108 equation:

2x+12=3x^2-108

We move all terms to the left:

2x+12-(3x^2-108)=0

We get rid of parentheses

-3x^2+2x+108+12=0

We add all the numbers together, and all the variables

-3x^2+2x+120=0

a = -3; b = 2; c = +120;
Δ = b2-4ac
Δ = 22-4·(-3)·120
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-38}{2*-3}=\frac{-40}{-6}
=6+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+38}{2*-3}=\frac{36}{-6}
=-6
$