Answer
No real solutions.
Work Step by Step
We solve:
$x(x+1)+2=0$
$x^{2}+x+2=0$
We solve using the quadratic formula ($a=1,\ b=1,\ c=2$):
$\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
$\displaystyle x=\frac{-1\pm\sqrt{(1)^{2}-4*1*2}}{2(1)}=\frac{-1\pm\sqrt{-7}}{2}$
However, we note that the discriminant is negative. Therefore, there are no real solutions.