Y=-16x^2+60x+80

Solution for Y=-16x^2+60x+80 equation:

=-16Y^2+60Y+80

We move all terms to the left:

-(-16Y^2+60Y+80)=0

We get rid of parentheses

16Y^2-60Y-80=0

a = 16; b = -60; c = -80;
Δ = b2-4ac
Δ = -602-4·16·(-80)
Δ = 8720
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:

$\sqrt{\Delta}=\sqrt{8720}=\sqrt{16*545}=\sqrt{16}*\sqrt{545}=4\sqrt{545}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{545}}{2*16}=\frac{60-4\sqrt{545}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{545}}{2*16}=\frac{60+4\sqrt{545}}{32}
$