Solve the following equation:
$28 x^{3} - 9 x^{2} + 1 = 0$ .

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Solution

Given equation, $28 x^{3} - 9 x^{2} + 1 = 0$
$⟹ 28 x^{3} - 16 x^{2} + 7 x^{2} + 4 x - 4 x + 1 = 0 ⟹ (4 x + 1) (7 x^{2} - 4 x + 1) = 0$
Solving the quadratic equation, we have $x = \frac{2 \pm \sqrt{3} i}{7}$

$∴$ roots of the given equation are $x = \frac{- 1}{4}, \frac{2 \pm \sqrt{3} i}{7}$

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