w(w+8)=240

Solution for w(w+8)=240 equation:

w(w+8)=240

We move all terms to the left:

w(w+8)-(240)=0

We multiply parentheses

w^2+8w-240=0

a = 1; b = 8; c = -240;
Δ = b2-4ac
Δ = 82-4·1·(-240)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-32}{2*1}=\frac{-40}{2}
=-20
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+32}{2*1}=\frac{24}{2}
=12
$