You don't say what restrictions there are on a, b and c. Integers, rational, all positive etc?
I don't think that there are any all integer solutions, nor any all positive rational solutions. There are however a whole stack of mixed positive/negative rational solutions, here are the first few.
a = 7/2, b = -13/6, c = 2/3
a = 14/3, b = -4, c = -5/3
a = 8/3, b = 5/2, c =-7/6
a = 6, b = -14/3, c = -13/3
a = 29/6, b = -10/3, c = -7/2.
Bertie
