[tex]4 \sqrt{3}x^2+5x-2 \sqrt{3}=0\\
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\Delta=5^2-4*4 \sqrt{3}* (-2\sqrt{3} )\\
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\Delta=25+96=121\\
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x=\frac{-5 \pm \sqrt{121}}{2*4 \sqrt{3} }=\frac{-5 \pm 11}{8 \sqrt3}\\
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x_1=\frac{-5-11}{8\sqrt3}=-\frac{16}{8\sqrt3}=-\frac{16\sqrt3}{24}=-\frac{2\sqrt3}{3}\\
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x_2=\frac{-5+11}{8\sqrt3}=\frac{6}{8\sqrt3}=\frac{6\sqrt3}{24}=\frac{\sqrt3}{4}\\
[/tex]
