2w(120-2w)=120

Solution for 2w(120-2w)=120 equation:

2w(120-2w)=120

We move all terms to the left:

2w(120-2w)-(120)=0

We add all the numbers together, and all the variables

2w(-2w+120)-120=0

We multiply parentheses

-4w^2+240w-120=0

a = -4; b = 240; c = -120;
Δ = b2-4ac
Δ = 2402-4·(-4)·(-120)
Δ = 55680
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:

$\sqrt{\Delta}=\sqrt{55680}=\sqrt{64*870}=\sqrt{64}*\sqrt{870}=8\sqrt{870}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-8\sqrt{870}}{2*-4}=\frac{-240-8\sqrt{870}}{-8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+8\sqrt{870}}{2*-4}=\frac{-240+8\sqrt{870}}{-8}
$