Non-Linear Equations: Root of 3rd order polynomial equation

Solve the 3rd order polynomial equation shown below.
1.5x3 - 7x2 - 5.8x + 5 = 0
/* Root of 3rd order polynomial */

1.5*x^3 - 7*x^2 - 5.8*x + 5 = 0
Explanation

^ represents a power.

The iterative method is necessary to solve non-linear equations, and initial estimate values are specified for the calculation.

If you do not specify an initial estimate value in the RESET statement, then the default value (0) will automatically be set.

This cubic equation contains 3 roots and if this is executed as is, only one of them will be solved.

Enter equations and click on the [Solve] button.

/* Root of 3rd order polynomial equation */ 1.5*x^3 - 7*x^2 - 5.8*x + 5 = 0
/* Root of 3rd order polynomial */

eq: 1.5*x^3 - 7*x^2 - 5.8*x + 5 = 0

RESET x#10 BY eq
Explanation

To solve the other two roots, initial estimate values must be given by adding the RESET statement as shown above. # means an initial value, and in the BY clause, the equation that verifies the convergence is specified.

eq is the label attached to the equation.

Enter equations and click on the [Solve] button.

/* Root of 3rd order polynomial equation */ eq: 1.5*x^3 - 7*x^2 - 5.8*x + 5 = 0 RESET x#10 BY eq

Sample problem

The following sample problems will help you understand how EQUATRAN-G works.

Linear equations: Tsuru-Kame-Zan (Japanese traditional problem, means problem of cranes and tortoises); Nutrients problem
Non-linear equations: Root of 3rd order polynomial equation; Loan calculation
Ordinary differential equations: 2nd order ordinary differential equation
Optimization and least square problems: Approximation in 3rd order polynomial equation