2x^2+2x-2016=2017

Solution for 2x^2+2x-2016=2017 equation:

2x^2+2x-2016=2017

We move all terms to the left:

2x^2+2x-2016-(2017)=0

We add all the numbers together, and all the variables

2x^2+2x-4033=0

a = 2; b = 2; c = -4033;
Δ = b2-4ac
Δ = 22-4·2·(-4033)
Δ = 32268
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32268}=\sqrt{4*8067}=\sqrt{4}*\sqrt{8067}=2\sqrt{8067}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{8067}}{2*2}=\frac{-2-2\sqrt{8067}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{8067}}{2*2}=\frac{-2+2\sqrt{8067}}{4}
$