x^2+2x=319

Solution for x^2+2x=319 equation:

x^2+2x=319

We move all terms to the left:

x^2+2x-(319)=0

a = 1; b = 2; c = -319;
Δ = b2-4ac
Δ = 22-4·1·(-319)
Δ = 1280
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:

$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-16\sqrt{5}}{2*1}=\frac{-2-16\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+16\sqrt{5}}{2*1}=\frac{-2+16\sqrt{5}}{2}
$