You can't use static equations to determine stability because stability is an inherently dynamic phenomenon.
Again, consider the case of a marble sitting at the bottom of a bowl or balanced at the top of a ball. In both cases they are in static equilibrium. The forces are balanced and there is no reason for the ball to do anything other than sit there and look stupid.
The difference is when the ball is perturbed slightly from that equilibrium position. In one case the forces that result return the ball toward the equilibrium position and in the other the forces drive it further away. Determining which is which cannot be done by just finding the point at which the forces are balanced, which is the same result in either case.
Whether the output is negative for a positive input has nothing to do with it. Look up the circuit for the classic non-inverting opamp circuit.
Closed loop gain equations are always for circuits that exhibit negative feedback (I'm pretty sure that's a true statement, but it's good enough for the circuits you are talking about). If the circuit has positive feedback then there is no closed loop gain because the circuit is unstable.
Again, consider the case of a marble sitting at the bottom of a bowl or balanced at the top of a ball. In both cases they are in static equilibrium. The forces are balanced and there is no reason for the ball to do anything other than sit there and look stupid.
The difference is when the ball is perturbed slightly from that equilibrium position. In one case the forces that result return the ball toward the equilibrium position and in the other the forces drive it further away. Determining which is which cannot be done by just finding the point at which the forces are balanced, which is the same result in either case.
Whether the output is negative for a positive input has nothing to do with it. Look up the circuit for the classic non-inverting opamp circuit.
Closed loop gain equations are always for circuits that exhibit negative feedback (I'm pretty sure that's a true statement, but it's good enough for the circuits you are talking about). If the circuit has positive feedback then there is no closed loop gain because the circuit is unstable.