Because that is what "intercept" means- the points where the graph crosses or "intercepts" the x-axis. The fact the roots of (2/3)x^2- 12x+ 50= 0 at x= 9+ sqrt(6) and x= 9- sqrt(x) means that the graph "intercepts" the x-axis at (9+ sqrt(6), 0) and (9- sqrt(6), 0).

(If I were you I would NOT approximate 9+ sqrt(6) by 11.4 and 9- sqrt(6) by 6.6. Surely, it is not that hard to use the actual values?)