Y=-2x^2+36x-159

Solution for Y=-2x^2+36x-159 equation:

=-2Y^2+36Y-159

We move all terms to the left:

-(-2Y^2+36Y-159)=0

We get rid of parentheses

2Y^2-36Y+159=0

a = 2; b = -36; c = +159;
Δ = b2-4ac
Δ = -362-4·2·159
Δ = 24
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:

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