x^2+2x=684

Solution for x^2+2x=684 equation:

x^2+2x=684

We move all terms to the left:

x^2+2x-(684)=0

a = 1; b = 2; c = -684;
Δ = b2-4ac
Δ = 22-4·1·(-684)
Δ = 2740
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:

$\sqrt{\Delta}=\sqrt{2740}=\sqrt{4*685}=\sqrt{4}*\sqrt{685}=2\sqrt{685}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{685}}{2*1}=\frac{-2-2\sqrt{685}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{685}}{2*1}=\frac{-2+2\sqrt{685}}{2}
$