120=(w+2)w

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

120=(w+2)w

We move all terms to the left:

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


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

(w+2)w

We multiply parentheses

w^2+2w

Back to the equation:

-(w^2+2w)


We get rid of parentheses

-w^2-2w+120=0

We add all the numbers together, and all the variables

-1w^2-2w+120=0

a = -1; b = -2; c = +120;
Δ = b2-4ac
Δ = -22-4·(-1)·120
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-22}{2*-1}=\frac{-20}{-2}
=+10
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+22}{2*-1}=\frac{24}{-2}
=-12
$