A quadratic with complex roots

Discriminant. $\Delta=4-20=-16=(4i)^2$.

Roots.
$$x_1=\frac{-2+4i}{2}=-1+2i, \qquad x_2=\frac{-2-4i}{2}=-1-2i.$$

Conclusion. $x\in\{-1+2i,\,-1-2i\}$. Note that the roots are conjugate, as expected for a real polynomial.