Is this equation wrong?
Remember that current, in the conventional way, flows from positive to negative, which means the current flows from the greater voltage to a lower one.

In this case, \$I_3\$ flows downwards, from \$V_B\$ to \$V_A\$, which means \$V_B\$ is thought to be greater than \$V_A\$ although in the end of the circuit´s resolution you´ll find that it may not be true. Then \$I_3\$ it´s supposed to be \$\frac{V_A-V_B}{R_2}\$. Anyway, for writing the equations, the link you provided brings a correct reasoning.