Answer
$x=3\pm\sqrt{6}$
Work Step by Step
Using the completing the square method, then,
\begin{array}{l}
x^2-6x+3=0\\
x^2-6x=-3\\
x^2-6x+\left( \dfrac{-6}{2} \right)^2=-3+\left( \dfrac{-6}{2}\right)^2\\
x^2-6x+9=-3+9\\
\left( x-3 \right)^2=6\\
x-3=\pm\sqrt{6}\\
x=3\pm\sqrt{6}
.\end{array}
