34=w(2)+2+w

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

34=w(2)+2+w

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-w^2-w-2+34=0

We add all the numbers together, and all the variables

-1w^2-1w+32=0

a = -1; b = -1; c = +32;
Δ = b2-4ac
Δ = -12-4·(-1)·32
Δ = 129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{129}}{2*-1}=\frac{1-\sqrt{129}}{-2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{129}}{2*-1}=\frac{1+\sqrt{129}}{-2}
$