468=3x^2+3x

Solution for 468=3x^2+3x equation:

468=3x^2+3x

We move all terms to the left:

468-(3x^2+3x)=0

We get rid of parentheses

-3x^2-3x+468=0

a = -3; b = -3; c = +468;
Δ = b2-4ac
Δ = -32-4·(-3)·468
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-75}{2*-3}=\frac{-72}{-6}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+75}{2*-3}=\frac{78}{-6}
=-13
$