Y=-16x^2+32x+80

Solution for Y=-16x^2+32x+80 equation:

=-16Y^2+32Y+80

We move all terms to the left:

-(-16Y^2+32Y+80)=0

We get rid of parentheses

16Y^2-32Y-80=0

a = 16; b = -32; c = -80;
Δ = b2-4ac
Δ = -322-4·16·(-80)
Δ = 6144
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:

$\sqrt{\Delta}=\sqrt{6144}=\sqrt{1024*6}=\sqrt{1024}*\sqrt{6}=32\sqrt{6}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32\sqrt{6}}{2*16}=\frac{32-32\sqrt{6}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32\sqrt{6}}{2*16}=\frac{32+32\sqrt{6}}{32}
$