(20-0.5y)y=100

Solution for (20-0.5y)y=100 equation:

(20-0.5y)y=100

We move all terms to the left:

(20-0.5y)y-(100)=0

We add all the numbers together, and all the variables

(-0.5y+20)y-100=0

We multiply parentheses

0y^2+20y-100=0

We add all the numbers together, and all the variables

y^2+20y-100=0

a = 1; b = 20; c = -100;
Δ = b2-4ac
Δ = 202-4·1·(-100)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20\sqrt{2}}{2*1}=\frac{-20-20\sqrt{2}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20\sqrt{2}}{2*1}=\frac{-20+20\sqrt{2}}{2}
$