w(50-2w)=250

Solution for w(50-2w)=250 equation:

w(50-2w)=250

We move all terms to the left:

w(50-2w)-(250)=0

We add all the numbers together, and all the variables

w(-2w+50)-250=0

We multiply parentheses

-2w^2+50w-250=0

a = -2; b = 50; c = -250;
Δ = b2-4ac
Δ = 502-4·(-2)·(-250)
Δ = 500
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:

$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-10\sqrt{5}}{2*-2}=\frac{-50-10\sqrt{5}}{-4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+10\sqrt{5}}{2*-2}=\frac{-50+10\sqrt{5}}{-4}
$