Y=-2x^2+12x+108

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

=-2Y^2+12Y+108

We move all terms to the left:

-(-2Y^2+12Y+108)=0

We get rid of parentheses

2Y^2-12Y-108=0

a = 2; b = -12; c = -108;
Δ = b2-4ac
Δ = -122-4·2·(-108)
Δ = 1008
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{7}}{2*2}=\frac{12-12\sqrt{7}}{4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{7}}{2*2}=\frac{12+12\sqrt{7}}{4}
$