Question

$\sqrt{3}{x}^2+11x+6\sqrt{3}=0$

Answer 1

$$\begin{gathered} \mathrm{Given}: \\ \sqrt{3}{x}^2+11x+6\sqrt{3}=0 \\ \Rightarrow \sqrt{3}{x}^2+9x+2x+6\sqrt{3}=0 \\ \Rightarrow \sqrt{3}x(x+3\sqrt{3})+2(x+3\sqrt{3})=0 \\ \Rightarrow (x+3\sqrt{3})(\sqrt{3}x+2)=0 \\ \Rightarrow x+3\sqrt{3}=0\text{or}\sqrt{3}x+2=0 \\ \Rightarrow x=-3\sqrt{3}\text{or}x=\frac{-2}{\sqrt{3}}=\frac{-2\times \sqrt{3}}{\sqrt{3}\times \sqrt{3}}=\frac{-2\sqrt{3}}{3} \\ \text{Hence, the roots of the equation are}-\text{3}\sqrt{3}\text{and}\frac{-2\sqrt{3}}{3}. \end{gathered}$$