OK, When you are solving for H, don't make the problem more complex by increasing the number of H. In your first and second equations of the last post, there are just one H, but you made the problem more complex by increasing the number of H in equation 3. Don't do that. Instead, (1/R) - 1/(R+H) = (V^2)/(2gR^2) or, 1/(R+H) = (1/R) - (V^2)/(2gR^2) or, 1/(R+H) = (2gR - V^2) / (2gR^2) or, H = (2gR^2)/(2gR-V^2) - R or, H = (RV^2)/(2gR - V^2)