Solve the following equation:
$9^{{log}_{3} (1 - 2 x)} = 5 x^{2} - 5$

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Solution

$3^{2 {log}_{3} (1 - 2 x)} = 5 x^{2} - 5 (1 - 2 x)^{2} = 5 x^{2} - 5 1 + 4 x^{2} - 4 x = 5 x^{2} - 5 x^{2} + 4 x - 6 = 0 x = \frac{- 4 \pm \sqrt{16 + 24}}{2} = \frac{- 4 \pm 2 \sqrt{10}}{2} = - 2 \pm \sqrt{10}$

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