Y=-x2-8x+32

Solution for Y=-x2-8x+32 equation:

=-Y2-8Y+32

We move all terms to the left:

-(-Y2-8Y+32)=0

We add all the numbers together, and all the variables

-(-1Y^2-8Y+32)=0

We get rid of parentheses

1Y^2+8Y-32=0

We add all the numbers together, and all the variables

Y^2+8Y-32=0

a = 1; b = 8; c = -32;
Δ = b2-4ac
Δ = 82-4·1·(-32)
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{3}}{2*1}=\frac{-8-8\sqrt{3}}{2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{3}}{2*1}=\frac{-8+8\sqrt{3}}{2}
$