2w+2w(2w+1)=29

Solution for 2w+2w(2w+1)=29 equation:

2w+2w(2w+1)=29

We move all terms to the left:

2w+2w(2w+1)-(29)=0

We multiply parentheses

4w^2+2w+2w-29=0

We add all the numbers together, and all the variables

4w^2+4w-29=0

a = 4; b = 4; c = -29;
Δ = b2-4ac
Δ = 42-4·4·(-29)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{30}}{2*4}=\frac{-4-4\sqrt{30}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{30}}{2*4}=\frac{-4+4\sqrt{30}}{8}
$