Answer
$x=\{ -1,4 \}$
Work Step by Step
Isolating the radical expression and then squaring both sides, the solution to the given equation, $
x-\sqrt{13-3x} -3=0
,$ is
\begin{array}{l}\require{cancel}
x -3=\sqrt{13-3x}
\\\\
(x -3)^2=(\sqrt{13-3x})^2
\\\\
(x)^2+2(x)(-3)+(-3)^2=13-3x
\\\\
x^2-6x+9=13-3x
\\\\
x^2+(-6x+3x)+(9-13)=0
\\\\
x^2-3x-4=0
\\\\
(x-4)(x+1)=0
\\\\
x=\{ -1,4 \}
.\end{array}
