$$3^{1/2}x^2-8x+4\cdot3^{1/2} = 0$$
Answer
$$ \begin{matrix}x_1 = 4-2 \sqrt{ 3 } & x_2 = 4+2 \sqrt{ 3 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 3^{1/2}x^2-8x+4\cdot3^{1/2} &= 0&& \text{multiply ALL terms by } \color{blue}{ 2 }. \\[1 em]23^{1/2}x^2-2\cdot8x+2\cdot4\cdot3^{1/2} &= 2\cdot0&& \text{cancel out the denominators} \\[1 em]2x^2-16x+8 &= 0&& \\[1 em] \end{aligned} $$
$ 2x^{2}-16x+8 = 0 $ is a quadratic equation.
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