Solve the equation 27x2 – 10x + 1 = 0

The given quadratic equation is $27 x^{2}-10 x+1=0$

On comparing the given equation with $a x^{2}+b x+c=0$, we obtain

$a=27, b=-10$, and $c=1$

Therefore, the discriminant of the given equation is

$D=b^{2}-4 a c=(-10)^{2}-4 \times 27 \times 1=100-108=-8$

Therefore, the required solutions are

$\frac{-b \pm \sqrt{\mathrm{D}}}{2 a}=\frac{-(-10) \pm \sqrt{-8}}{2 \times 27}=\frac{10 \pm 2 \sqrt{2} i}{54}$   $[\sqrt{-1}=i]$

$=\frac{5 \pm \sqrt{2} i}{27}=\frac{5}{27} \pm \frac{\sqrt{2}}{27} i$