Are you looking for exact solutions? In that case you would need a calculator or software that can do symbolic manipulation (such as the TI-89). These are called computer algebra systems (CAS).

If you just want to approximate the solution of an equation numerically, then there are a couple of ways on the TI-83. First move everything in the equation to one side so that the expression is set equal to zero. Then do one of the following.

Use the Equation Solver: select 0:Solver from the MATH menu. Enter in the expression, and then press ENTER. A list of the variables will appear, and you may enter any known values. If you like, enter a guess for the value of the unknown variable (it will help the calculator solve it faster). If there is a specific range of values you want to consider, edit the bound; otherwise leave the default. Then highlight the variable you want to solve for, press ALPHA, and then press SOLVE (above the ENTER key).

Alternatively, enter your expression in the Y= editor, and graph it. Press 2nd and then CALC, and choose 2:zero. If you have multiple functions graphed, use the up and down arrows to cycle to the one you want. Then use the left and right arrows to set the lower and upper bounds for the search. Finally, make a guess for the zero. The cursor moves to the intercept, and the coordinates are given. The -coordinate is the one you want.

(And by the way, all of this is very easily found in the calculator's manual, which is itself easily found with Google)