w(w-12)=640

Solution for w(w-12)=640 equation:

w(w-12)=640

We move all terms to the left:

w(w-12)-(640)=0

We multiply parentheses

w^2-12w-640=0

a = 1; b = -12; c = -640;
Δ = b2-4ac
Δ = -122-4·1·(-640)
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-52}{2*1}=\frac{-40}{2}
=-20
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+52}{2*1}=\frac{64}{2}
=32
$