w(4+2w)=38

Solution for w(4+2w)=38 equation:

w(4+2w)=38

We move all terms to the left:

w(4+2w)-(38)=0

We add all the numbers together, and all the variables

w(2w+4)-38=0

We multiply parentheses

2w^2+4w-38=0

a = 2; b = 4; c = -38;
Δ = b2-4ac
Δ = 42-4·2·(-38)
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8\sqrt{5}}{2*2}=\frac{-4-8\sqrt{5}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8\sqrt{5}}{2*2}=\frac{-4+8\sqrt{5}}{4}
$