smc

Because the two points are on a diameter, the center must be halfway between them at the point $(4,3)$. The distance from $(0,0)$ to $(4,3)$ is 5 so the circle has radius 5. Thus, the equation of the circle is $(x-4{)}^2+(y-3{)}^2=25$. To find the x-intercept, y must be 0, so $(x-4{)}^2+(0-3{)}^2=25$, so $(x-4{)}^2=16$, $x-4=4$, $x=8,\boxed{8}$.