Y=-16x^2+160x+150

Solution for Y=-16x^2+160x+150 equation:

=-16Y^2+160Y+150

We move all terms to the left:

-(-16Y^2+160Y+150)=0

We get rid of parentheses

16Y^2-160Y-150=0

a = 16; b = -160; c = -150;
Δ = b2-4ac
Δ = -1602-4·16·(-150)
Δ = 35200
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:

$\sqrt{\Delta}=\sqrt{35200}=\sqrt{1600*22}=\sqrt{1600}*\sqrt{22}=40\sqrt{22}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-40\sqrt{22}}{2*16}=\frac{160-40\sqrt{22}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+40\sqrt{22}}{2*16}=\frac{160+40\sqrt{22}}{32}
$