First step, solve the square root:
[tex]\begin{gathered} \sqrt{x}=x-6 \\ (\sqrt{x})^2=(x-6)^2 \\ x=(x-6)^2 \\ x=x^2-12x+36 \end{gathered}[/tex]Now, we group the terms with "x" on the same side:
[tex]\begin{gathered} x^2-12x+36-x=0 \\ x^2-13x+36=0 \end{gathered}[/tex]Next, we use the quadratic formula to solve the equation:
[tex]\begin{gathered} x=\frac{13\pm\sqrt{13^2-4*36}}{2} \\ x=\frac{13\pm\sqrt{25}}{2} \\ x=\frac{13\pm5}{2} \\ x=9\text{ or }x=4 \end{gathered}[/tex]Hence, the answer is x=9 or x=4
