Step 1:

The bridge network is shown below.

Apply KVL for the loop ABDA

Apply KVL for the loop BCDB

Apply KVL for the loop ADCEA

Step 2:

Now solve the three equations.

Multiply equation (1) with 2.

Subtract equation (2) from equation (4).

Substitute equation (5) in equation (3).

Substitute equation (5).

Substitute and in equation (1).

The current values are  , and .

Therefore Current in the branch BD is .

Solution:

Therefore Current in the branch BD is .