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Solving a Quadratic Equation by Factorization Method

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Question

Solve the following quadratic equation for $x : 4 \sqrt{3 x^{2}} + 5 x - 2 \sqrt{3} = 0$

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Solution

$4 \sqrt{3 x^{2}} + 5 x - 2 \sqrt{3} = 0 4 \sqrt{3 x^{2}} + 8 x - 3 x - 2 \sqrt{3} = 0 4 x (\sqrt{3} x + 2) - \sqrt{3} (\sqrt{3} + 2) = 0 (4 x - \sqrt{3}) (\sqrt{3} x + 2) = 0 ∴ x = \frac{\sqrt{3}}{4} o r x = - \frac{2}{\sqrt{3}}$

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