Apr 2, 2018

$x = 8$

#### Explanation:

One way to solve $\sqrt{3 x + 1} = x - 3$ is by squaring both equation terms or

$3 x + 1 = {\left(x - 3\right)}^{2}$

This operation is responsible for the introduction of strange solutions because solving

${x}^{2} - 6 x + 9 = 3 x + 1 \Rightarrow {x}^{2} - 9 x + 8 = 0$ we have

${x}^{2} - 6 x + 9 = \left(x - 1\right) \left(x - 8\right) = 0$ and after substitution in the initial equation we conclude that $x = 1$ is not feasible and the solution is $x = 8$