2w(w+10)=50

Solution for 2w(w+10)=50 equation:

2w(w+10)=50

We move all terms to the left:

2w(w+10)-(50)=0

We multiply parentheses

2w^2+20w-50=0

a = 2; b = 20; c = -50;
Δ = b2-4ac
Δ = 202-4·2·(-50)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20\sqrt{2}}{2*2}=\frac{-20-20\sqrt{2}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20\sqrt{2}}{2*2}=\frac{-20+20\sqrt{2}}{4}
$