(4+2w)w=160

Solution for (4+2w)w=160 equation:

(4+2w)w=160

We move all terms to the left:

(4+2w)w-(160)=0

We add all the numbers together, and all the variables

(2w+4)w-160=0

We multiply parentheses

2w^2+4w-160=0

a = 2; b = 4; c = -160;
Δ = b2-4ac
Δ = 42-4·2·(-160)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-36}{2*2}=\frac{-40}{4}
=-10
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+36}{2*2}=\frac{32}{4}
=8
$