w(2w+4)=44

Solution for w(2w+4)=44 equation:

w(2w+4)=44

We move all terms to the left:

w(2w+4)-(44)=0

We multiply parentheses

2w^2+4w-44=0

a = 2; b = 4; c = -44;
Δ = b2-4ac
Δ = 42-4·2·(-44)
Δ = 368
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:

$\sqrt{\Delta}=\sqrt{368}=\sqrt{16*23}=\sqrt{16}*\sqrt{23}=4\sqrt{23}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{23}}{2*2}=\frac{-4-4\sqrt{23}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{23}}{2*2}=\frac{-4+4\sqrt{23}}{4}
$