w(2w+10)=1000

Solution for w(2w+10)=1000 equation:

w(2w+10)=1000

We move all terms to the left:

w(2w+10)-(1000)=0

We multiply parentheses

2w^2+10w-1000=0

a = 2; b = 10; c = -1000;
Δ = b2-4ac
Δ = 102-4·2·(-1000)
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-90}{2*2}=\frac{-100}{4}
=-25
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+90}{2*2}=\frac{80}{4}
=20
$