w*(w+40)=6000

Solution for w*(w+40)=6000 equation:

w(w+40)=6000

We move all terms to the left:

w(w+40)-(6000)=0

We multiply parentheses

w^2+40w-6000=0

a = 1; b = 40; c = -6000;
Δ = b2-4ac
Δ = 402-4·1·(-6000)
Δ = 25600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25600}=160$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-160}{2*1}=\frac{-200}{2}
=-100
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+160}{2*1}=\frac{120}{2}
=60
$