Answer
$x=\dfrac{3}{2}\pm \dfrac{i\sqrt{15}}{6}$
Work Step by Step
Using the completing the square method, the solution set to the equation $
3x^2-9x+8=0
$ is
\begin{array}{l}
x^2-3x+\dfrac{8}{3}=0
\text{... divide both sides by 3}
\\\\
x^2-3x=-\dfrac{8}{3}
\\\\
x^2-3x+\left( \dfrac{-3}{2} \right)^2=-\dfrac{8}{3}+\left( \dfrac{-3}{2} \right)^2
\\\\
x^2-3x+\dfrac{9}{4}=-\dfrac{8}{3}+\dfrac{9}{4}
\\\\
x^2-3x+\dfrac{9}{4}=\dfrac{-32+27}{12}
\\\\
\left( x-\dfrac{3}{2} \right)^2=\dfrac{-5}{12}
\\\\
x-\dfrac{3}{2}=\pm\sqrt{\dfrac{-5}{12}}
\\\\
x-\dfrac{3}{2}=\pm i\sqrt{\dfrac{5}{4\cdot3}}
\\\\
x-\dfrac{3}{2}=\pm \dfrac{i}{2}\sqrt{\dfrac{5}{3}}
\\\\
x-\dfrac{3}{2}=\pm \dfrac{i}{2}\sqrt{\dfrac{5}{3}\cdot\dfrac{3}{3}}
\\\\
x-\dfrac{3}{2}=\pm \dfrac{i}{2}\sqrt{\dfrac{15}{9}}
\\\\
x-\dfrac{3}{2}=\pm \dfrac{i\sqrt{15}}{6}
\\\\
x=\dfrac{3}{2}\pm \dfrac{i\sqrt{15}}{6}
.\end{array}
