6000=(w+40)w

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

6000=(w+40)w

We move all terms to the left:

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


We calculate terms in parentheses: -((w+40)w), so:

(w+40)w

We multiply parentheses

w^2+40w

Back to the equation:

-(w^2+40w)


We get rid of parentheses

-w^2-40w+6000=0

We add all the numbers together, and all the variables

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