Solve the equation : $\;\sqrt{3}x^{2}-\sqrt{2}x+3\sqrt{3}=0\;$

Question

$(a)\;\large\frac{1 \pm \sqrt{34} i}{3\sqrt{2}}\qquad(b)\;\large\frac{-1 \pm \sqrt{3} i}{-2}\qquad(c)\;\large\frac{\sqrt{2} \pm \sqrt{34} i}{2 \sqrt{3}}\qquad(d)\;\large\frac{-1 \pm \sqrt{7} i}{2 \sqrt{2}}$