Answer
$$x = \frac{5 \frac{+}{}\sqrt {13}}{6}$$
Work Step by Step
$3x^2 - 5x + 1 = 0$ is a quadratic function. Therefore, to solve for $x$ we can either use the Quadratic Formula or factorize the equation. Since $a\ne 1$ in this exercise, it's just easier to directly go ahead and use the Quadratic Formula $x = \frac{-b \frac{+}{}\sqrt {b^{2} - 4ac}}{2a}$:
$$x = \frac{-b \frac{+}{}\sqrt {b^{2} - 4ac}}{2a}$$
$$x = \frac{-(-5) \frac{+}{}\sqrt {(-5)^{2} - 4(3)(1)}}{2(3)}$$
$$x = \frac{5 \frac{+}{}\sqrt {25 - 12}}{6}$$
$$x = \frac{5 \frac{+}{}\sqrt {13}}{6}$$
