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Question
Solve for x:
Solution
\[\sqrt{3} x^2 - 2\sqrt{2}x - 2\sqrt{3} = 0\]
\[ \Rightarrow \sqrt{3} x^2 - 3\sqrt{2}x + \sqrt{2}x - 2\sqrt{3} = 0\]
\[ \Rightarrow \sqrt{3}x\left( x - \sqrt{6} \right) + \sqrt{2}\left( x - \sqrt{6} \right) = 0\]
\[ \Rightarrow \left( \sqrt{3}x + \sqrt{2} \right)\left( x - \sqrt{6} \right) = 0\]
\[ \Rightarrow x = - \frac{\sqrt{2}}{\sqrt{3}} \text{or}\ x = \sqrt{6}\]
\[ \Rightarrow x = - \sqrt{\frac{2}{3}} \text{or}\ x = \sqrt{6}\]
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