Consider this circuit

As can be seen in the picture I want to calculate the voltage(the red one).I think the english term for this is terminal voltage? Maybe not correct me if I am wrong;

Now this was my approach. First I wanted to calculate the resistance of the entire circuit and I did it like this. The resistor of 10 Ohm (lets call him R1) and the 20 Ohm resistor (lets call him R2) are parallel; So their voltage should be R12 = 6,66 Ohm. Than that should be in series with the 30 Ohm resistor (R3) and the total resitance of the circuit should be Rtotal = 36,6 Ohm

Now I can calculate the current I,as I = Uq(15V)/Rtotal = 0,40 A.

So now I used the Kirchoffs 1 and 2nd law to set up my equations. For the current law (I think that is the english term) I said that the current leaving R1 and flowing into the upper junction is the same as the currents leaving the upper junction; hence

I1 = I2 + I3;

For the Kirchoffs Loop Law I made two loops; for the left one I got this

U1 + U2 - Uq = 0; (if we take the direction clockwise)

For the right one I got this

U3 +U - U2 = 0;

Now since I know the current I should be able to calculate U1 as U1 = R1 * I; that should be 4V. Now I can solve my first loop equation (the left one)

4 + U2 - 15 = 0 --> U2 = 9V

Okay so now I know; U1 = 4V, U2 = 9V I1 = 0,40A

To solve my second loop I need U3. I can calculate U3 as U3 = I3 * R3. I can get I3 if I find I2,for that I used the fact that I know U2 and R2;

I2 = U2/R2 = 0,45A. Now I plug that into the very first equation I1 = I2 + I3 --> I3 = -0,05 A.

Plug that into U3 = -1,5 V

And now plug this into my second loop equation

-1,5 + U - 9 = 0 --> U = 10,5 V

Now the solution should be 10V. Where did I make mistake? I double checked my work by the equations and they should be correct (considering the direction I choose at the loops).Did I make an error at the beginning? Maybe I calculate Rtotal wrong;

Any insight is helpful.

Many thanks!