Answer
$$x_1=0$$
$$x_2\approx0.01255$$
Work Step by Step
$x^3-6x^2+9x=\sqrt{x}$
To find the solution, we can graph the equations separated by the equal sign separately.
$x^3-6x^2+9x$ is represented as the Blue graph on the image above.
$\sqrt{x}$ is represented as the Red graph.
(Note! the image above is zoomed-in near the origin of coordinate plane. Otherwise it is hard to notice the intersections, since it happens very close to $0$)
The solutions are intersections of these graphs, those are the points $A$ and $B$. So we have another two solutions:
$x_1=0$
$x_2\approx0.01255$