84^2=w*(2w+2)

Solution for 84^2=w*(2w+2) equation:

84^2=w(2w+2)

We move all terms to the left:

84^2-(w(2w+2))=0

We add all the numbers together, and all the variables

-(w(2w+2))+7056=0


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

w(2w+2)

We multiply parentheses

2w^2+2w

Back to the equation:

-(2w^2+2w)


We get rid of parentheses

-2w^2-2w+7056=0

a = -2; b = -2; c = +7056;
Δ = b2-4ac
Δ = -22-4·(-2)·7056
Δ = 56452
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:

$\sqrt{\Delta}=\sqrt{56452}=\sqrt{4*14113}=\sqrt{4}*\sqrt{14113}=2\sqrt{14113}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{14113}}{2*-2}=\frac{2-2\sqrt{14113}}{-4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{14113}}{2*-2}=\frac{2+2\sqrt{14113}}{-4}
$