Y=-16x^2+32x+1584

Solution for Y=-16x^2+32x+1584 equation:

=-16Y^2+32Y+1584

We move all terms to the left:

-(-16Y^2+32Y+1584)=0

We get rid of parentheses

16Y^2-32Y-1584=0

a = 16; b = -32; c = -1584;
Δ = b2-4ac
Δ = -322-4·16·(-1584)
Δ = 102400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{102400}=320$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-320}{2*16}=\frac{-288}{32}
=-9
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+320}{2*16}=\frac{352}{32}
=11
$