Answer
$x=2$ or $x=\displaystyle \frac{1}{3}$
Work Step by Step
$ 3x^{2}-7x+2=0\qquad$... solve with the Quadractic formula. $a=3,\ b=-7,\ c=2$
$ x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\qquad$... substitute $b$ for $-7,\ a$ for $3$ and $c$ for $2$.
$ x=\displaystyle \frac{-(-7)\pm\sqrt{(-7)^{2}-4\cdot(3)\cdot 2}}{2\cdot 3}\qquad$... simplify.
$x=\displaystyle \frac{7\pm\sqrt{49-24}}{6}$
$x=\displaystyle \frac{7\pm\sqrt{25}}{6}$
$ x=\displaystyle \frac{7\pm 5}{6}\qquad$... the symbol $\pm$ indicates two solutions.
$x=\displaystyle \frac{7+5}{6}$ or $x=\displaystyle \frac{7-5}{6}$
$x=2$ or $x=\displaystyle \frac{1}{3}$