Answer
$x=\displaystyle \frac{5+\sqrt{13}}{6}\approx 1.434$
or $x=\displaystyle \frac{5-\sqrt{13}}{6}\approx 0.232$
Work Step by Step
$3x^{2}-5x+1=0$
To factor the trinomial we search for
factors of $3\times 1$ whose sum is $-5$ ...
... none
We can always use the quadratic formula:
(For $ax^{2}+bx+c=0,\ x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$ )
$x=\displaystyle \frac{-(-5)\pm\sqrt{(-5)^{2}-4(3)(1)}}{2(3)}$
$x=\displaystyle \frac{5\pm\sqrt{25-12}}{6}$
$x=\displaystyle \frac{5+\sqrt{13}}{6}$ or $x=\displaystyle \frac{5-\sqrt{13}}{6}$
$x\approx 1.434$ or $x\approx 0.232$
