Opamp Question not clear with currents

[Vihaan]

I am unclear of how to mark the currents, i have written the equations the problem is 4 unkowns and 3 equations, how do i solve?

[ledtester]

You have the necessary number of equations.

Use KCL at nodes A, B, C and D and also use the fact that C = D through the opamp action.
This gives you 5 equations and 5 unknowns (A, B, C, D and Vout).

Example KCL equation for node A:

-5.5ma + (B-A)/22k + (D-A)/22k = 0

[Vihaan]

Ok, thank you very much the below equations considering A,B,C,D and C = D
The updated solution is i have attached, the voltages are very high the opamp will saturate to 9V.
VA = 821.33V, VB = 902V, VD=861V, VC = 861V, Vout = 1723V.
I made LTspice and it matches with the results.
 

[Analog Kid]

You do realize that those voltages are impossible, yes?

Sorry I can't help you here—this stuff is all above my pay grade—but I do recognize out-of-bounds conditions when I see them.

Also, beware (or more correctly, be wary) of simulations.

[RFDx]

The updated solution is i have attached, the voltages are very high the opamp will saturate to 9V.
VA = 821.33V, VB = 902V, VD=861V, VC = 861V, Vout = 1723V.

The calculated theoretical output voltage of 1723V is fine. It's obviously a trick question. There's no need to do any calculations at all because the voltage developed across the 22k sense resistor by a loop current of 5.5mA is already way beyond the two op-amp supply rails. You can immediately tell that the output voltage of the differential amplifier, which by the way has substantial gain, will go to one of the rails and you just have to think about if it's +9V or -9V.

[PCB.Wiz]

I am unclear of how to mark the currents, i have written the equations the problem is 4 unkowns and 3 equations, how do i solve?

A quick sanity check shows 5.5mA is a nonsense test, that’s over 100V!
It may be a ‘mu’ symbol got mangled to ‘m’, or a value is wrong.
Run the numbers again with a 5.5 micro amps, or change the shunt to 22 ohms.