w(w+9)=400

Solution for w(w+9)=400 equation:

w(w+9)=400

We move all terms to the left:

w(w+9)-(400)=0

We multiply parentheses

w^2+9w-400=0

a = 1; b = 9; c = -400;
Δ = b2-4ac
Δ = 92-4·1·(-400)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-41}{2*1}=\frac{-50}{2}
=-25
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+41}{2*1}=\frac{32}{2}
=16
$