48=(2w+8)(w)

Solution for 48=(2w+8)(w) equation:

48=(2w+8)(w)

We move all terms to the left:

48-((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+48=0

a = -2; b = -8; c = +48;
Δ = b2-4ac
Δ = -82-4·(-2)·48
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{7}}{2*-2}=\frac{8-8\sqrt{7}}{-4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{7}}{2*-2}=\frac{8+8\sqrt{7}}{-4}
$