w(2w-15)=500

Solution for w(2w-15)=500 equation:

w(2w-15)=500

We move all terms to the left:

w(2w-15)-(500)=0

We multiply parentheses

2w^2-15w-500=0

a = 2; b = -15; c = -500;
Δ = b2-4ac
Δ = -152-4·2·(-500)
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-65}{2*2}=\frac{-50}{4}
=-12+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+65}{2*2}=\frac{80}{4}
=20
$