w(w+80)=240

Solution for w(w+80)=240 equation:

w(w+80)=240

We move all terms to the left:

w(w+80)-(240)=0

We multiply parentheses

w^2+80w-240=0

a = 1; b = 80; c = -240;
Δ = b2-4ac
Δ = 802-4·1·(-240)
Δ = 7360
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:

$\sqrt{\Delta}=\sqrt{7360}=\sqrt{64*115}=\sqrt{64}*\sqrt{115}=8\sqrt{115}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-8\sqrt{115}}{2*1}=\frac{-80-8\sqrt{115}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+8\sqrt{115}}{2*1}=\frac{-80+8\sqrt{115}}{2}
$