120=(6w+2w)(w)

Solution for 120=(6w+2w)(w) equation:

120=(6w+2w)(w)

We move all terms to the left:

120-((6w+2w)(w))=0

We add all the numbers together, and all the variables

-((+8w)w)+120=0


We calculate terms in parentheses: -((+8w)w), so:

(+8w)w

We multiply parentheses

8w^2

Back to the equation:

-(8w^2)


a = -8; b = 0; c = +120;
Δ = b2-4ac
Δ = 02-4·(-8)·120
Δ = 3840
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:

$\sqrt{\Delta}=\sqrt{3840}=\sqrt{256*15}=\sqrt{256}*\sqrt{15}=16\sqrt{15}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{15}}{2*-8}=\frac{0-16\sqrt{15}}{-16}
=-\frac{16\sqrt{15}}{-16}
=-\frac{\sqrt{15}}{-1}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{15}}{2*-8}=\frac{0+16\sqrt{15}}{-16}
=\frac{16\sqrt{15}}{-16}
=\frac{\sqrt{15}}{-1}
$