2(5+w)2w=34

Solution for 2(5+w)2w=34 equation:

2(5+w)2w=34

We move all terms to the left:

2(5+w)2w-(34)=0

We add all the numbers together, and all the variables

2(w+5)2w-34=0

We multiply parentheses

4w^2+20w-34=0

a = 4; b = 20; c = -34;
Δ = b2-4ac
Δ = 202-4·4·(-34)
Δ = 944
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:

$\sqrt{\Delta}=\sqrt{944}=\sqrt{16*59}=\sqrt{16}*\sqrt{59}=4\sqrt{59}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{59}}{2*4}=\frac{-20-4\sqrt{59}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{59}}{2*4}=\frac{-20+4\sqrt{59}}{8}
$