2x^2+2x=312

Solution for 2x^2+2x=312 equation:

2x^2+2x=312

We move all terms to the left:

2x^2+2x-(312)=0

a = 2; b = 2; c = -312;
Δ = b2-4ac
Δ = 22-4·2·(-312)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-50}{2*2}=\frac{-52}{4}
=-13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+50}{2*2}=\frac{48}{4}
=12
$