GEH^2 = 2(M-C)^2/[M+C]
GEH^2*[M+C} = 2(M-C)^2
GEH^2*M + GEH^2*C = 2[M^2 - 2MC + C^2]
M[GEH^2 + 4C] = 2M^2 + 2C^2
M = [2M^2 + 2C^2]/[GEH^2 + 4C]
= 2M^2/[GEH^2 + 4C] + 2C^2/[GEH^2 + 4C]
Let a = 2/[GEH^2 + 4C] and c = 2C^2/[GEH^2 + 4C]
then we have the quadratic equation:
aM^2 - M + c = 0 which will have either no real solutions, one real solution, or two real solutions.
Depending on the context of the situation and on the C and GEH values, if you get two solutions you will probably eliminate one and get the right answer.