Answer
{$\dfrac{1 - i\sqrt {107}}{6},\dfrac{1+ i\sqrt {107}}{6}$}
Work Step by Step
Re-write the given equation as: $3x^2-x+9=0$
Factorize the expression with the help of quadratic formula. Quadratic formula suggests that $x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$
This implies that $x=\dfrac{-(-1) \pm \sqrt{(-1)^2-4(3)(9)}}{2(3)}$
or, $x=\dfrac{1 \pm \sqrt {-107}}{6}$
or, $x=\dfrac{1 \pm i\sqrt {107}}{6}$
or, $x=\dfrac{1 + i\sqrt {107}}{6},\dfrac{1 - i\sqrt {107}}{6}$
Hence, our solution set is: {$\dfrac{1 - i\sqrt {107}}{6},\dfrac{1+ i\sqrt {107}}{6}$}
