120=(2w+4)w

Solution for 120=(2w+4)w equation:

120=(2w+4)w

We move all terms to the left:

120-((2w+4)w)=0


We calculate terms in parentheses: -((2w+4)w), so:

(2w+4)w

We multiply parentheses

2w^2+4w

Back to the equation:

-(2w^2+4w)


We get rid of parentheses

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

a = -2; b = -4; c = +120;
Δ = b2-4ac
Δ = -42-4·(-2)·120
Δ = 976
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:

$\sqrt{\Delta}=\sqrt{976}=\sqrt{16*61}=\sqrt{16}*\sqrt{61}=4\sqrt{61}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{61}}{2*-2}=\frac{4-4\sqrt{61}}{-4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{61}}{2*-2}=\frac{4+4\sqrt{61}}{-4}
$