(w+20)w=400

Solution for (w+20)w=400 equation:

(w+20)w=400

We move all terms to the left:

(w+20)w-(400)=0

We multiply parentheses

w^2+20w-400=0

a = 1; b = 20; c = -400;
Δ = b2-4ac
Δ = 202-4·1·(-400)
Δ = 2000
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:

$\sqrt{\Delta}=\sqrt{2000}=\sqrt{400*5}=\sqrt{400}*\sqrt{5}=20\sqrt{5}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20\sqrt{5}}{2*1}=\frac{-20-20\sqrt{5}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20\sqrt{5}}{2*1}=\frac{-20+20\sqrt{5}}{2}
$