Obtain the node voltages in the following circuit:

Please show me the step by step solution to find the nodes $($V$1$ and V$2)$ voltages. the answers should be $($V$1=5\mathrm{.}45$ and V$2=-43\mathrm{.}63).$

$-$ Please also clarify how we find the current directions and how to use KCL

Thanks!