The particle is coming in from infinity, so the classical turning point is the greatest solution $r_*$ to your second equation. This corresponds to the first place beyond which, if the particle continued moving toward the origin, its kinetic energy would be negative.

The particle is coming in from infinity, so the classical turning point is the greatest solution $r_*$ to your second equation. This corresponds to the first place beyond which, if the particle continued moving toward the origin, its radial kinetic energy would be negative. (The angular part of the kinetic energy is part of the effective potential.)