One obvious solution is following: x = 1.
If you plot the graphs, it will be obvious, that except x = 1 there are no other solutions.
For any arbitrary constants there is no analytical solution. Instead, solutions are based on some iterating converging process until you reach needed precision.
Yes, it is legal to apply tan to both parts. When two values are equal, then their tan values are equal, too. But if you are going to use that to get an equation that is easier to solve, pay attention, because another equation can have more solutions than your original equation and you will have to filter them to find out the solution of your original equation.