Y=-16X^2+160x+50

Solution for Y=-16X^2+160x+50 equation:

=-16Y^2+160Y+50

We move all terms to the left:

-(-16Y^2+160Y+50)=0

We get rid of parentheses

16Y^2-160Y-50=0

a = 16; b = -160; c = -50;
Δ = b2-4ac
Δ = -1602-4·16·(-50)
Δ = 28800
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:

$\sqrt{\Delta}=\sqrt{28800}=\sqrt{14400*2}=\sqrt{14400}*\sqrt{2}=120\sqrt{2}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-160)-120\sqrt{2}}{2*16}=\frac{160-120\sqrt{2}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-160)+120\sqrt{2}}{2*16}=\frac{160+120\sqrt{2}}{32}
$