Y=100-(8x^2)+32x

Solution for Y=100-(8x^2)+32x equation:

=100-(8Y^2)+32Y

We move all terms to the left:

-(100-(8Y^2)+32Y)=0

We get rid of parentheses

8Y^2-32Y-100=0

a = 8; b = -32; c = -100;
Δ = b2-4ac
Δ = -322-4·8·(-100)
Δ = 4224
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:

$\sqrt{\Delta}=\sqrt{4224}=\sqrt{64*66}=\sqrt{64}*\sqrt{66}=8\sqrt{66}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{66}}{2*8}=\frac{32-8\sqrt{66}}{16}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{66}}{2*8}=\frac{32+8\sqrt{66}}{16}
$