Question

A 390.45 kg satellite is geosynchronous orbit around the Earth stays over the same spot and takes 24 hours to make one revolution.  Given the following data, determine the satellite

Answer 1

Your method is correct. Of course, the small m's cancel out. I believe that I get the correct answer using your method.

w^2*(r+h)=G*Me/(r+h)^2

where
w: orbital velocity in radians per second
r: earth radius
Me: mass of Earth (from google)
G: gravitational constant (from google)

substitute w = 2*pi/T, where T is the rotation time of the Earth (for more precision, you should use the sidereal day, which is 23 hours, 56 minutes, 4 seconds ).

We can now solve for h to get the following.

h = (1/2pi)*2^(1/3)*(G*Me*T^2*pi)^(1/3)-r

put the value and find h