2(2w+4)=8(w+6)w=

Solution for 2(2w+4)=8(w+6)w= equation:

2(2w+4)=8(w+6)w=

We move all terms to the left:

2(2w+4)-(8(w+6)w)=0

We multiply parentheses

4w-(8(w+6)w)+8=0


We calculate terms in parentheses: -(8(w+6)w), so:

8(w+6)w

We multiply parentheses

8w^2+48w

Back to the equation:

-(8w^2+48w)


We get rid of parentheses

-8w^2+4w-48w+8=0

We add all the numbers together, and all the variables

-8w^2-44w+8=0

a = -8; b = -44; c = +8;
Δ = b2-4ac
Δ = -442-4·(-8)·8
Δ = 2192
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:

$\sqrt{\Delta}=\sqrt{2192}=\sqrt{16*137}=\sqrt{16}*\sqrt{137}=4\sqrt{137}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{137}}{2*-8}=\frac{44-4\sqrt{137}}{-16}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{137}}{2*-8}=\frac{44+4\sqrt{137}}{-16}
$