HP -32S Owner's Manual page 119

The following program evaluates this function:
R01 LBL R
R02 RCL X
R83 5
R04 -
R05 RCLx
R06 10
R07 -
R08 RCLx X
R09 20
R10 +
Rll RTN
X
A plot of this function is:
*3-5*2-10*+20
The plot indicates that there are three roots because the curve crosses
the x-axis three times. The calculator can find all three roots if you
run SOLVE three times and supply different initial guesses each time.
(For more information, see 'Choosing Initial Guesses for SOLVE.*)
Enter the above program (LBL R). The graph shows that the first root
is somewhere between x = —3 and x = —2, the second root is be
tween 1 and 2, and the third root is between 6 and 7. Put each set of
guesses in the variable X and in the X-register, then solve for X.
7: Solving for an Unknown Variable in an Equation 117