w+34=w2

Solution for w+34=w2 equation:

w+34=w2

We move all terms to the left:

w+34-(w2)=0

We add all the numbers together, and all the variables

-1w^2+w+34=0

a = -1; b = 1; c = +34;
Δ = b2-4ac
Δ = 12-4·(-1)·34
Δ = 137
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{137}}{2*-1}=\frac{-1-\sqrt{137}}{-2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{137}}{2*-1}=\frac{-1+\sqrt{137}}{-2}
$