-4=2(w+2)4w

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

-4=2(w+2)4w

We move all terms to the left:

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


We calculate terms in parentheses: -(2(w+2)4w), so:

2(w+2)4w

We multiply parentheses

8w^2+16w

Back to the equation:

-(8w^2+16w)


We get rid of parentheses

-8w^2-16w-4=0

a = -8; b = -16; c = -4;
Δ = b2-4ac
Δ = -162-4·(-8)·(-4)
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{2}}{2*-8}=\frac{16-8\sqrt{2}}{-16}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{2}}{2*-8}=\frac{16+8\sqrt{2}}{-16}
$