52=(2w+8)(w)

Solution for 52=(2w+8)(w) equation:

52=(2w+8)(w)

We move all terms to the left:

52-((2w+8)(w))=0


We calculate terms in parentheses: -((2w+8)w), so:

(2w+8)w

We multiply parentheses

2w^2+8w

Back to the equation:

-(2w^2+8w)


We get rid of parentheses

-2w^2-8w+52=0

a = -2; b = -8; c = +52;
Δ = b2-4ac
Δ = -82-4·(-2)·52
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{30}}{2*-2}=\frac{8-4\sqrt{30}}{-4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{30}}{2*-2}=\frac{8+4\sqrt{30}}{-4}
$