Y=-16x^2+32x+64

Solution for Y=-16x^2+32x+64 equation:

=-16Y^2+32Y+64

We move all terms to the left:

-(-16Y^2+32Y+64)=0

We get rid of parentheses

16Y^2-32Y-64=0

a = 16; b = -32; c = -64;
Δ = b2-4ac
Δ = -322-4·16·(-64)
Δ = 5120
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:

$\sqrt{\Delta}=\sqrt{5120}=\sqrt{1024*5}=\sqrt{1024}*\sqrt{5}=32\sqrt{5}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32\sqrt{5}}{2*16}=\frac{32-32\sqrt{5}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32\sqrt{5}}{2*16}=\frac{32+32\sqrt{5}}{32}
$