Answer
The solutions are $x=1\pm\dfrac{\sqrt{6}}{3}$
Work Step by Step
$3x^{2}=6x-1$
Take all terms to the left side:
$3x^{2}-6x+1=0$
Solve this equation using the quadratic formula, which is $x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}$.
For this equation, $a=3,$ $b=-6$ and $c=1$
Substitute the known values into the formula and evaluate:
$x=\dfrac{-(-6)\pm\sqrt{(-6)^{2}-4(3)(1)}}{2(3)}=\dfrac{6\pm\sqrt{36-12}}{6}=...$
$...=\dfrac{6\pm\sqrt{24}}{6}=\dfrac{6\pm2\sqrt{6}}{6}=3\pm\dfrac{\sqrt{6}}{3}$
