MathNet 2007-part-03 — 185 problems (EN–VI) Question 38

Find all positive real numbers $x$ satisfying the equation $$x + \left[ \frac{x}{3} \right] = \left[ \frac{2x}{3} \right] + \left[ \frac{3x}{5} \right],$$ where $[x]$ is the largest integer not exceeding $x$.