Solution
We want to solve for x in
[tex]x-6=\sqrt[]{3x}[/tex]So we will have
[tex]\begin{gathered} x-6=\sqrt[]{3x} \\ \text{Square both sides} \\ (x-6)^2=(\sqrt[]{3x})^2 \\ x^2-12x+36=3x \\ x^2-15x+36=0 \\ x^2-12x-3x+36=0_{} \\ x(x-12)-3(x-12)=0 \\ (x-12)(x-3)=0 \\ \text{Either} \\ x-12=0 \\ x=12 \\ or \\ x-3=0 \\ x=3 \end{gathered}[/tex]Therefore, the answer is
[tex]x=12,3[/tex]