Y=-16x^2+240x+115

Solution for Y=-16x^2+240x+115 equation:

=-16Y^2+240Y+115

We move all terms to the left:

-(-16Y^2+240Y+115)=0

We get rid of parentheses

16Y^2-240Y-115=0

a = 16; b = -240; c = -115;
Δ = b2-4ac
Δ = -2402-4·16·(-115)
Δ = 64960
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:

$\sqrt{\Delta}=\sqrt{64960}=\sqrt{64*1015}=\sqrt{64}*\sqrt{1015}=8\sqrt{1015}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-8\sqrt{1015}}{2*16}=\frac{240-8\sqrt{1015}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+8\sqrt{1015}}{2*16}=\frac{240+8\sqrt{1015}}{32}
$