Solve this

Solution:

Given:

$3 x^{2}-4 x+\frac{20}{3}=0$

Multiplying both the sides by 3 we get,

$9 x^{2}-12 x+20=0$

Solution of a general quadratic equation $a x^{2}+b x+c=0$ is given by:

$x=\frac{-b \pm \sqrt{\left(b^{2}-4 a c\right)}}{2 a}$

$\Rightarrow x=\frac{-(-12) \pm \sqrt{(-12)^{2}-(4 \times 9 \times 20)}}{2 \times 9}$

$\Rightarrow x=\frac{12 \pm \sqrt{144-720}}{18}$

$\Rightarrow x=\frac{12 \pm \sqrt{-576}}{18}$

$\Rightarrow x=\frac{12 \pm 24 i}{18}$

$x=\frac{12}{18} \pm \frac{24}{18} i$

$\Rightarrow \quad x=\frac{2}{3} \pm \frac{4}{3} i$

Ans: $x=\frac{2}{3}+\frac{4}{3} i$ and $x=\frac{2}{3}-\frac{4}{3} i$