Guess a Solution and Solve the Equation
When using the TI83 Plus graphing calculator’s Equation Solver, you need to guess at a solution by assigning a value to the variable you’re solving for. Any value in the interval defined by the bound variable will do. If your guess is close to the solution, the calculator quickly solves the equation; if it’s not, it may take the calculator a while to solve the equation.
If your equation has more than one solution, the calculator will find the one closest to your guess.
If the variable you’re solving for is assigned a value (guess) that isn’t in the interval defined by the bound variable, then you get the ERR: BAD GUESS error message.
To solve an equation, follow these steps:

Use
to place the cursor anywhere in the line that contains the variable you’re solving for.

Press [ALPHA][ENTER] to solve the equation.
The third picture shows this procedure; the square indicator shown next to the L indicates that L is the variable just solved for. The left – rt value that appears at the bottom of this picture evaluates the two sides of the equation (using the values assigned to the variables) and displays the difference — that is, the accuracy of this solution. A left – rt value of zero indicates an exact solution.
If you get the ERR: NO SIGN CHNG error message when you attempt to solve an equation using the Equation Solver, then the equation has no real solutions in the interval defined by the bound variable.
To find other solutions to an equation, first find one solution to the equation.
Then enter a new guess for the solution you’re seeking, or, in the bound variable, enter the bounds of an interval that possibly contains a different solution. In the second picture a new guess for the solution is entered.
After making a new guess or after redefining the bound variable, follow the step for finding the first equation:

Use
to place the cursor anywhere in the line that contains the variable you’re solving for.

Press [ALPHA][ENTER] to solve the equation.
The third picture shows this procedure; the square indicator shown next to the L indicates that L is the variable just solved for. The left – rt value that appears at the bottom of this picture evaluates the two sides of the equation (using the values assigned to the variables) and displays the difference — that is, the accuracy of this solution. A left – rt value of zero indicates an exact solution.