w(2w-8)=280

Solution for w(2w-8)=280 equation:

w(2w-8)=280

We move all terms to the left:

w(2w-8)-(280)=0

We multiply parentheses

2w^2-8w-280=0

a = 2; b = -8; c = -280;
Δ = b2-4ac
Δ = -82-4·2·(-280)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-48}{2*2}=\frac{-40}{4}
=-10
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+48}{2*2}=\frac{56}{4}
=14
$