w(w+40)=4000

Solution for w(w+40)=4000 equation:

w(w+40)=4000

We move all terms to the left:

w(w+40)-(4000)=0

We multiply parentheses

w^2+40w-4000=0

a = 1; b = 40; c = -4000;
Δ = b2-4ac
Δ = 402-4·1·(-4000)
Δ = 17600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{17600}=\sqrt{1600*11}=\sqrt{1600}*\sqrt{11}=40\sqrt{11}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40\sqrt{11}}{2*1}=\frac{-40-40\sqrt{11}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40\sqrt{11}}{2*1}=\frac{-40+40\sqrt{11}}{2}
$