Answer
$\left\{\dfrac{1-\sqrt{23}i}{6},\dfrac{1+\sqrt{23}i}{6}\right\}$
Work Step by Step
The equation is in standard form:
$$3x^2-x+2=0.$$
To solve the equation $ax^2+bx+c=0$ we will use the quadratic formula:
$$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$$
Identify $a$, $b$, $c$:
$$\begin{align*}
a&=3\\
b&=-1\\
c&=2.
\end{align*}$$
We solve the given equation by substituting the values of $a$, $b$, $c$ in the quadratic formula:
$$\begin{align*}
x&=\dfrac{-(-1)\pm\sqrt{(-1)^2-4(3)(2)}}{2(3)}\\
&=\dfrac{1\pm\sqrt{23}i}{6}.
\end{align*}$$
The solution set of the equation is:
$$\left\{\dfrac{1-\sqrt{23}i}{6},\dfrac{1+\sqrt{23}i}{6}\right\}.$$
