Steps Key Sequence Screens
Method 1: Use to find solutions of f1(x) = f2(x).
Example: Solve x3 + 3x2 + 2x = 5.
1. Input f1(x) into Y1 (in this example Y1=x3+3x2+2x)  
2. Input f2(x) into Y2 (in this example Y2=5)  
3. Graph Press GRAPH
4. Find Intersection Press 2nd, then TRACE (for CALC)
  Press 5 (for intersect)
  Press ENTER two (2) times
  Move cursor close to intersection, then press ENTER
NOTE: The point of intersection is on the bottom of the TI83 screen. The solution is the x-coordinate of the intersection. Repeat Step #4 for other intersections.
Method 2: Use to find one root of f1(x) – f2(x) = 0
Example: Solve x3 + 2x = –3x2.
Rewrite the equation so that all terms are on one side: x3 + 3x2 + 2x = 0
1. Set Up Solve() Function Press 2nd, then 0 (for CATALOG()
  Press LN key to scroll down to S
  Scroll down to solve(
  Press ENTER
2. Type in Function  
3. Input Independent Variable Press comma, then variable solving for, then comma
4. Input Guess Type number near one of the roots, then right parenthesis
5. Execute Press ENTER
NOTE: This method finds only one solution. You will need to input several guesses to find all the roots.