108=w^2+4w

Solution for 108=w^2+4w equation:

108=w^2+4w

We move all terms to the left:

108-(w^2+4w)=0

We get rid of parentheses

-w^2-4w+108=0

We add all the numbers together, and all the variables

-1w^2-4w+108=0

a = -1; b = -4; c = +108;
Δ = b2-4ac
Δ = -42-4·(-1)·108
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{-(-4)-8\sqrt{7}}{2*-1}=\frac{4-8\sqrt{7}}{-2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8\sqrt{7}}{2*-1}=\frac{4+8\sqrt{7}}{-2}
$