Solve $\;x^{2} + x + 1=0 $

Question

$(a)\;\large\frac{\pm \sqrt{3}i}{2}\qquad(b)\;\large\frac{1+ \sqrt{3}i}{2}\qquad(c)\;\large\frac{-1\pm \sqrt{3}i}{5}\qquad(d)\;\large\frac{-1\pm \sqrt{3}i}{2}$