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

Question

$(a)\;\large\frac{-1 \pm \sqrt{7} i}{-3}\qquad(b)\;\large\frac{-1 \pm \sqrt{3} i}{-2}\qquad(c)\;\large\frac{-1 \pm \sqrt{5} i}{2 \sqrt{2}}\qquad(d)\;\large\frac{-1 \pm \sqrt{7} i}{2 \sqrt{2}}$