120=w(2w+1)

Solution for 120=w(2w+1) equation:

120=w(2w+1)

We move all terms to the left:

120-(w(2w+1))=0


We calculate terms in parentheses: -(w(2w+1)), so:

w(2w+1)

We multiply parentheses

2w^2+w

Back to the equation:

-(2w^2+w)


We get rid of parentheses

-2w^2-w+120=0

We add all the numbers together, and all the variables

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

a = -2; b = -1; c = +120;
Δ = b2-4ac
Δ = -12-4·(-2)·120
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-31}{2*-2}=\frac{-30}{-4}
=7+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+31}{2*-2}=\frac{32}{-4}
=-8
$