The solution method depends a little on what you are solving for, and whether you want a transient or a steady-state solution. I assume because there is "only one battery" that it is a DC circuit and you want a steady-state solution.
In the general case, you ...
In the general case, you ...
- identify the branches of the circuit
- associate a current variable with each branch
- identify each node of the circuit (place where 2 or more branches meet)
- associate a voltage variable with each node
- write the equation for each branch current in terms of the voltages at the nodes it is connected between
- write the equation summing the currents into each node, recognizing that the sum of the currents into the node is zero.
- solve the set of equations you have written.