w(w+4)=320

Solution for w(w+4)=320 equation:

w(w+4)=320

We move all terms to the left:

w(w+4)-(320)=0

We multiply parentheses

w^2+4w-320=0

a = 1; b = 4; c = -320;
Δ = b2-4ac
Δ = 42-4·1·(-320)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-36}{2*1}=\frac{-40}{2}
=-20
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+36}{2*1}=\frac{32}{2}
=16
$