3x-216=-3x^2

Solution for 3x-216=-3x^2 equation:

3x-216=-3x^2

We move all terms to the left:

3x-216-(-3x^2)=0

We get rid of parentheses

3x^2+3x-216=0

a = 3; b = 3; c = -216;
Δ = b2-4ac
Δ = 32-4·3·(-216)
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-51}{2*3}=\frac{-54}{6}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+51}{2*3}=\frac{48}{6}
=8
$