2x^2+2x=31

Solution for 2x^2+2x=31 equation:

2x^2+2x=31

We move all terms to the left:

2x^2+2x-(31)=0

a = 2; b = 2; c = -31;
Δ = b2-4ac
Δ = 22-4·2·(-31)
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6\sqrt{7}}{2*2}=\frac{-2-6\sqrt{7}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6\sqrt{7}}{2*2}=\frac{-2+6\sqrt{7}}{4}
$