solving for r for an equation?

Unfortunately question can be read in a number of different ways due to incorrect presentation.

Must be clarified.

Is it meant to be :-

(1/3) r^(3/2) + (3/2) r^(1/2) = 0

Let us try this :-

2 r^(3/2) + 9 r^(1/2) = 0
Let r^(1/2) = x

2x³ + 9x = 0
x (2x² + 9) = 0
x = 0

r^(1/2) = 0
NO SOLUTION.

The main point to emerge from this is that questions must be presented such they can be read in one and only one way.
Brackets MUST be used in the proper manner.