Y=-4x^2+24x+32

Solution for Y=-4x^2+24x+32 equation:

=-4Y^2+24Y+32

We move all terms to the left:

-(-4Y^2+24Y+32)=0

We get rid of parentheses

4Y^2-24Y-32=0

a = 4; b = -24; c = -32;
Δ = b2-4ac
Δ = -242-4·4·(-32)
Δ = 1088
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:

$\sqrt{\Delta}=\sqrt{1088}=\sqrt{64*17}=\sqrt{64}*\sqrt{17}=8\sqrt{17}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{17}}{2*4}=\frac{24-8\sqrt{17}}{8}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{17}}{2*4}=\frac{24+8\sqrt{17}}{8}
$