Solve the equation. x - 6 = √(3x)

Question

Solve the equation.
`x - 6 = √(3x)`

Answer 1

We want to solve for x in

`x-6=\sqrt[]{3x}`

So we will have

`\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}`

Therefore, the answer is

`x=12,3`