100=-2x^2+32x

Solution for 100=-2x^2+32x equation:

100=-2x^2+32x

We move all terms to the left:

100-(-2x^2+32x)=0

We get rid of parentheses

2x^2-32x+100=0

a = 2; b = -32; c = +100;
Δ = b2-4ac
Δ = -322-4·2·100
Δ = 224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{14}}{2*2}=\frac{32-4\sqrt{14}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{14}}{2*2}=\frac{32+4\sqrt{14}}{4}
$