x^2+2x=238

Solution for x^2+2x=238 equation:

x^2+2x=238

We move all terms to the left:

x^2+2x-(238)=0

a = 1; b = 2; c = -238;
Δ = b2-4ac
Δ = 22-4·1·(-238)
Δ = 956
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:

$\sqrt{\Delta}=\sqrt{956}=\sqrt{4*239}=\sqrt{4}*\sqrt{239}=2\sqrt{239}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{239}}{2*1}=\frac{-2-2\sqrt{239}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{239}}{2*1}=\frac{-2+2\sqrt{239}}{2}
$