X^2+2x=216

Solution for X^2+2x=216 equation:

X^2+2X=216

We move all terms to the left:

X^2+2X-(216)=0

a = 1; b = 2; c = -216;
Δ = b2-4ac
Δ = 22-4·1·(-216)
Δ = 868
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:

$\sqrt{\Delta}=\sqrt{868}=\sqrt{4*217}=\sqrt{4}*\sqrt{217}=2\sqrt{217}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{217}}{2*1}=\frac{-2-2\sqrt{217}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{217}}{2*1}=\frac{-2+2\sqrt{217}}{2}
$