Answer
The solutions of the equation $3{{x}^{2}}-6x+2=0$ are $\frac{3+\sqrt{3}}{3}$ and $\frac{3-\sqrt{3}}{3}$.
Work Step by Step
Solve the equation $3{{x}^{2}}-6x+2=0$ by finding the roots of the quadratic equation of $ x $ as follows:
And compare with the equation $ a{{x}^{2}}+bx+c=0$,
$ a=3$, $ b=-6$ and $ c=2$
Therefore, we have
$\begin{align}
& x=\frac{-b\pm \sqrt{{{b}^{2}}-4ac}}{2a} \\
& =\frac{-\left( -6 \right)\pm \sqrt{{{\left( -6 \right)}^{2}}-4\left( 3 \right)\left( 2 \right)}}{2\left( 3 \right)} \\
& =\frac{6\pm \sqrt{36-24}}{6} \\
& =\frac{6\pm \sqrt{12}}{6}
\end{align}$
Then, simplify further:
$ x=\frac{3+\sqrt{3}}{3}$, $ x=\frac{3-\sqrt{3}}{3}$
Thus, the solutions of the equation $3{{x}^{2}}-6x+2=0$ are $\frac{3+\sqrt{3}}{3}$ and $\frac{3-\sqrt{3}}{3}$.
