Answer
See below.
Work Step by Step
Each rock hits the surface when $h=0$ and the $t$'s must be positive. Thus when we take the square root, we only need to consider the positive cases. Hence:
Earth: $0=-\frac{32}{2}t^2+150\\16t^2=150\\t^2=\frac{150}{16}=\frac{75}{8}\\t=\sqrt{\frac{75}{8}}$
Mars: $0=-\frac{12}{2}t^2+150\\6t^2=150\\t^2=\frac{150}{6}=25\\t=\sqrt{25}=5$
Jupiter: $0=-\frac{76}{2}t^2+150\\38t^2=150\\t^2=\frac{150}{38}=\frac{75}{19}\\t=\sqrt{\frac{75}{19}}$
Saturn: $0=-\frac{30}{2}t^2+150\\15t^2=150\\t^2=\frac{150}{15}=10\\t=\sqrt{10}$
Pluto: $0=-\frac{2}{2}t^2+150\\t^2=150\\t=\sqrt{150}$
