6x-108=-2x^2

Solution for 6x-108=-2x^2 equation:

6x-108=-2x^2

We move all terms to the left:

6x-108-(-2x^2)=0

We get rid of parentheses

2x^2+6x-108=0

a = 2; b = 6; c = -108;
Δ = b2-4ac
Δ = 62-4·2·(-108)
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*2}=\frac{-36}{4}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+30}{2*2}=\frac{24}{4}
=6
$