Since the bridge is not accelerating in an upward or downward direction, the system is in equilibrium and therefore Fnet must be zero. From this, we can produce the following equation:
We need either Fa or Fb to get this equation down any further. To get one of them, let's turn to the other fact we know about equilibrium, the net torque must be zero. Pick a pivot point that is at either force A or B so that one of the unknowns is eliminated and solve for the other. We'll put the pivot at A.
Now we can find A by placing the newly found B value into the equation:
