\(x = \dfrac{{5 \pm \sqrt {13} }}{6}\)

\begin{array}{l}
3 x^{2}-5 x+1=0 \\
a=3, b=-5, c=1 \\
x=\dfrac{-b \pm \sqrt{b^{2}-4ac}}{2 a}\\
x=\dfrac{5 \pm \sqrt{25-4 \times 3 \times 1}}{2 \times 3} \\
x=\dfrac{5 \pm \sqrt{13}}{6}
\end{array}