Answer
a) The solutions are $x \approx 0.057 $ and $x \approx 1.943$
b) There are no real solution.
Work Step by Step
a) We solve for $x$ in the equation $3 x^2-6 x+\frac{1}{3}=0$ using the quadratic formula with $a=3, b=-6$ and $c=1/3$.
$$
\begin{aligned}
& x=\frac{6 \pm \sqrt{6^2-4 \cdot 3 \cdot \frac{1}{3}}}{2 \cdot 3} \\
& x=\frac{6 \pm \sqrt{36-4}}{6}=\frac{6 \pm \sqrt{32}}{6} \\
& x=1 \pm \frac{4 \sqrt{2}}{6} \\
& x \approx 0.057 \text { or } x \approx 1.943 .
\end{aligned}
$$
The solutions are $x \approx 0.057 $ and $x \approx 1.943$.
b)
We solve for $x$ in the equation $2 x^2-5.1 x+7.2=0$ using the quadratic formula with $a=2, b=-5.1$ and $c=7.2$.
$$
x=\frac{5.1 \pm \sqrt{5.1^2-4 \cdot 2 \cdot 7.2}}{2 \cdot 2} =\frac{5.1 \pm \sqrt{-31.59}}{4}
$$
There are no real solution.
