Solving for  yields two solutions.  They must both be analyzed to determine which is the physical solution.  One will usually be a subsonic root and the other a supersonic root.  If it is not clear which value of velocity is correct, the second law of thermodynamics may be applied.
Second law of thermodynamics:
The values   and   are unknown and may be dropped from the formulation.  The value of entropy is not necessary, only that the value is positive.
One possible unreal solution for the stream thrust averaged velocity yields a negative entropy.  Another method of determining the proper solution is to take a simple average of the velocity and determining which value is closer to the stream thrust averaged velocity.