w(8+2w)=960

Solution for w(8+2w)=960 equation:

w(8+2w)=960

We move all terms to the left:

w(8+2w)-(960)=0

We add all the numbers together, and all the variables

w(2w+8)-960=0

We multiply parentheses

2w^2+8w-960=0

a = 2; b = 8; c = -960;
Δ = b2-4ac
Δ = 82-4·2·(-960)
Δ = 7744
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7744}=88$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-88}{2*2}=\frac{-96}{4}
=-24
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+88}{2*2}=\frac{80}{4}
=20
$