x^2+2x=1300

Solution for x^2+2x=1300 equation:

x^2+2x=1300

We move all terms to the left:

x^2+2x-(1300)=0

a = 1; b = 2; c = -1300;
Δ = b2-4ac
Δ = 22-4·1·(-1300)
Δ = 5204
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:

$\sqrt{\Delta}=\sqrt{5204}=\sqrt{4*1301}=\sqrt{4}*\sqrt{1301}=2\sqrt{1301}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{1301}}{2*1}=\frac{-2-2\sqrt{1301}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{1301}}{2*1}=\frac{-2+2\sqrt{1301}}{2}
$