Solve the quadratic equation $5 x^{2} = - 16 x - 12$ by factorisation method.

x = 2, \frac{6}{5}

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x = 2, \frac{5}{6}

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x = - 2, - \frac{5}{6}

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x = - 2, - \frac{6}{5}

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Solution

The correct option is D $x = - 2, - \frac{6}{5}$
Given equation is $5 x^{2} = - 16 x - 12$
$\Rightarrow 5 x^{2} + 16 x + 12 = 0$
$\Rightarrow 5 x^{2} + 10 x + 6 x + 12 = 0$
$\Rightarrow 5 x (x + 2) + 6 (x + 2) = 0$
$\Rightarrow (x + 2) (5 x + 6) = 0$
$\Rightarrow x + 2 = 0$
$\Rightarrow x = - 2$
$= 5 x + 6 = 0 \Rightarrow x = - \frac{6}{5}$
$∴ x = - 2$ or $x = \frac{- 6}{5}$

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