Find the roots of the equation $3 x^{2} + 7 x - 20 = 0$ by the method of completing square?

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Solution

$3 x^{2} + 7 x - 20 = 0$
$(\sqrt{3} x)^{2} + 2 (\sqrt{3} x) (\frac{7}{2 \sqrt{3}}) + {(\frac{7}{2 \sqrt{3}})}^{2} - {(\frac{7}{2 \sqrt{3}})}^{2} - 20 = 0$
${(\sqrt{3} x + \frac{7}{2 \sqrt{3}})}^{2} - \frac{49}{12} - 20 = 0$
${(\sqrt{3} x + \frac{7}{2 \sqrt{3}})}^{2} - (\frac{49 + 240}{12}) = 0$
${(\sqrt{3} x + \frac{7}{2 \sqrt{3}})}^{2} - \frac{289}{12} = 0$
${(\sqrt{3} x + \frac{7}{2 \sqrt{3}})}^{2} - {(\frac{17}{\sqrt{12}})}^{2} = 0$
$(\sqrt{3} x + \frac{7}{2 \sqrt{3}} + \frac{17}{\sqrt{12}}) (\sqrt{3} x + \frac{7}{2 \sqrt{3}} - \frac{17}{\sqrt{12}}) = 0$

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