Answer
$$x=\frac{1}{6}\pm\frac{\sqrt{11}}{6}i$$
Work Step by Step
To solve for $x$ first rewrite in standard quadratic equation form: $ax^2 + bx +c=0$
$3x^2-x+1=0$
where $a=3$, $b=-1$, and $c=1$
now, apply the quadratic formula: $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$
$$x=\frac{(-)(-1)\pm\sqrt{(-1)^2-4(3)(1)}}{2(3)}$$
$$x=\frac{1\pm\sqrt{1-12}}{6}$$
$$x=\frac{1\pm\sqrt{-11}}{6}$$
$$x=\frac{1\pm(i)\sqrt{11}}{6}$$
rewrite in standard form $a + bi$
$$x=\frac{1}{6}\pm\frac{\sqrt{11}}{6}i$$
