2x^2+2x=53

Solution for 2x^2+2x=53 equation:

2x^2+2x=53

We move all terms to the left:

2x^2+2x-(53)=0

a = 2; b = 2; c = -53;
Δ = b2-4ac
Δ = 22-4·2·(-53)
Δ = 428
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:

$\sqrt{\Delta}=\sqrt{428}=\sqrt{4*107}=\sqrt{4}*\sqrt{107}=2\sqrt{107}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{107}}{2*2}=\frac{-2-2\sqrt{107}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{107}}{2*2}=\frac{-2+2\sqrt{107}}{4}
$