2(4+9w)w=4

Solution for 2(4+9w)w=4 equation:

2(4+9w)w=4

We move all terms to the left:

2(4+9w)w-(4)=0

We add all the numbers together, and all the variables

2(9w+4)w-4=0

We multiply parentheses

18w^2+8w-4=0

a = 18; b = 8; c = -4;
Δ = b2-4ac
Δ = 82-4·18·(-4)
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{22}}{2*18}=\frac{-8-4\sqrt{22}}{36}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{22}}{2*18}=\frac{-8+4\sqrt{22}}{36}
$