In addition to solving expressions analytically, you can solve an equation graphically on the TI-89

 

First graph the equation you want to find the zero. 
Graph this equation in an appropriate window.  This a a graph of the equation in the zoom decimal window.  We know this is the behavior of the function over the entire domain since is always positive and therefore the function is always increasing. 
Next press 2nd CALC and access the command zero.
This will immediately take you to the graph and ask for a lower boundary for the zero.  Since there is only one zero in this equation the current lower boundary is acceptable.
Press enter to accept this lower boundary.  Then you will be asked for the right boundary.  Use the cursor keys to change the location of this right boundary.
When you press enter the calculator will calculate the zero for you equation in the selected window.

 

 

rev. 01/06/2007