w(2w+4)=240

Solution for w(2w+4)=240 equation:

w(2w+4)=240

We move all terms to the left:

w(2w+4)-(240)=0

We multiply parentheses

2w^2+4w-240=0

a = 2; b = 4; c = -240;
Δ = b2-4ac
Δ = 42-4·2·(-240)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-44}{2*2}=\frac{-48}{4}
=-12
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+44}{2*2}=\frac{40}{4}
=10
$