2x^2+2x=567

Solution for 2x^2+2x=567 equation:

2x^2+2x=567

We move all terms to the left:

2x^2+2x-(567)=0

a = 2; b = 2; c = -567;
Δ = b2-4ac
Δ = 22-4·2·(-567)
Δ = 4540
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:

$\sqrt{\Delta}=\sqrt{4540}=\sqrt{4*1135}=\sqrt{4}*\sqrt{1135}=2\sqrt{1135}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{1135}}{2*2}=\frac{-2-2\sqrt{1135}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{1135}}{2*2}=\frac{-2+2\sqrt{1135}}{4}
$