Solve this

Given:

$27 x^{2}+10 x+1=0$

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

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

$\Rightarrow x=\frac{-10 \pm \sqrt{(10)^{2}-(4 \times 27 \times 1)}}{2 \times 27}$

$\Rightarrow x=\frac{-10 \pm \sqrt{100-108}}{54}$

$\Rightarrow x=\frac{-10 \pm \sqrt{-8}}{54}$

$\Rightarrow \quad x=\frac{-10 \pm 2 \sqrt{2} i}{54}$

$\Rightarrow \quad x=-\frac{10}{54} \pm \frac{2 \sqrt{2}}{54} i$

Ans: $x=-\frac{5}{27}+\frac{\sqrt{2}}{27} i$ and $x=-\frac{5}{27}-\frac{\sqrt{2}}{27} i$