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

Question

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