Nodal Analysis of an Electric Circuit: Finding Node Voltages and Branch Currents

Find the node voltages and branch currents of the following electric circuit using nodal analysis:

According to the method of Nodal analysis, first of all we need to determine all the nodes of the circuit.  Then select the reference node which must be located to ground. After all denote all the unknown node voltages and all the branch currents.  Now the modified circuit looks like below:

Here we have four nodes in the circuit. The reference node is represented by yellow node. The pink color node voltage is known. So remaining two unknown nodes are represented by green color. 

The tricks is that the number of equations need to solve the problem equal to the number of unknown nodes. 

According to KCL, we get-