First, lets see what LTSpice says: (note I swapped the position of V2 and R2 to make it easier to visualize. I also labeled the nodes differently than you).
Now, using algebra:
Code:
Σ of currents into node B = 0
I1 + I2 + I3 = 0
I = V/R
[V(c)-V(b)] + [V(d) -V(b)] + [V(e)-(V(b)]
-------- ----------- ----------- = 0
2 4 6
6[-6-V(b)] + 3[4-V(b)] + 2[3-V(b)]
----------------------------------- = 0
12
-36 -6V(b) +12 -3V(b) +6 -2V(b) = 0
-3V(b) -6V(b) -2V(b) = 36 -6 -12
-11V(b) = 18
V(b) = -18/11 = -1.36363
Now that you know V(b), you can solve for the branch currents.
MikeMl, Ratchit, BrownOut, I'm very thankful to all of you. MikeMl, I do have some questions on LTspice which I will ask soon. I have it installed it on my computer but don't know how to use it. I also have Qucs program.