Y=-2x^2-24x+81

Solution for Y=-2x^2-24x+81 equation:

=-2Y^2-24Y+81

We move all terms to the left:

-(-2Y^2-24Y+81)=0

We get rid of parentheses

2Y^2+24Y-81=0

a = 2; b = 24; c = -81;
Δ = b2-4ac
Δ = 242-4·2·(-81)
Δ = 1224
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:

$\sqrt{\Delta}=\sqrt{1224}=\sqrt{36*34}=\sqrt{36}*\sqrt{34}=6\sqrt{34}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-6\sqrt{34}}{2*2}=\frac{-24-6\sqrt{34}}{4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+6\sqrt{34}}{2*2}=\frac{-24+6\sqrt{34}}{4}
$