w(w+2)=34

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

w(w+2)=34

We move all terms to the left:

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

We multiply parentheses

w^2+2w-34=0

a = 1; b = 2; c = -34;
Δ = b2-4ac
Δ = 22-4·1·(-34)
Δ = 140
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:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{35}}{2*1}=\frac{-2-2\sqrt{35}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{35}}{2*1}=\frac{-2+2\sqrt{35}}{2}
$