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

Question

$(a)\;\large\frac{-1\pm \sqrt{3} i}{4}\qquad(b)\;\large\frac{-1\pm \sqrt{5} i}{7}\qquad(c)\;\large\frac{-1\pm \sqrt{5} i}{4}\qquad(d)\;\large\frac{-1\pm \sqrt{7} i}{4}$