200=-w^2+100w

Solution for 200=-w^2+100w equation:

200=-w^2+100w

We move all terms to the left:

200-(-w^2+100w)=0

We get rid of parentheses

w^2-100w+200=0

a = 1; b = -100; c = +200;
Δ = b2-4ac
Δ = -1002-4·1·200
Δ = 9200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9200}=\sqrt{400*23}=\sqrt{400}*\sqrt{23}=20\sqrt{23}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-20\sqrt{23}}{2*1}=\frac{100-20\sqrt{23}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+20\sqrt{23}}{2*1}=\frac{100+20\sqrt{23}}{2}
$