2n^2-2n=34

Solution for 2n^2-2n=34 equation:

2n^2-2n=34

We move all terms to the left:

2n^2-2n-(34)=0

a = 2; b = -2; c = -34;
Δ = b2-4ac
Δ = -22-4·2·(-34)
Δ = 276
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{69}}{2*2}=\frac{2-2\sqrt{69}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{69}}{2*2}=\frac{2+2\sqrt{69}}{4}
$