Y=-16x2+32x

Solution for Y=-16x2+32x equation:

=-16Y^2+32Y

We move all terms to the left:

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

We get rid of parentheses

16Y^2-32Y=0

a = 16; b = -32; c = 0;
Δ = b2-4ac
Δ = -322-4·16·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-32}{2*16}=\frac{0}{32}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+32}{2*16}=\frac{64}{32}
=2
$