Y=-16x^2+32x+8

Solution for Y=-16x^2+32x+8 equation:

=-16Y^2+32Y+8

We move all terms to the left:

-(-16Y^2+32Y+8)=0

We get rid of parentheses

16Y^2-32Y-8=0

a = 16; b = -32; c = -8;
Δ = b2-4ac
Δ = -322-4·16·(-8)
Δ = 1536
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:

$\sqrt{\Delta}=\sqrt{1536}=\sqrt{256*6}=\sqrt{256}*\sqrt{6}=16\sqrt{6}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-16\sqrt{6}}{2*16}=\frac{32-16\sqrt{6}}{32}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+16\sqrt{6}}{2*16}=\frac{32+16\sqrt{6}}{32}
$