How to solve equation with a cube

For the solution of cubic equations developed by several mathematical methods. The method of substitution or replacement of cube auxiliary variable, and a number of iterative methods, in particular Newton's method. But the classical solution of the cubic equation is expressed in the use of the formulas of vieta and Cardano. The method of vieta-Cardano is based on the use of the formula of the cube of the sum of the coefficients and is applicable for any kind of cubic equation. To search for the roots of the equation , the entry must be represented in the form: x3+a*x2+b*x+c=0 where a is not zero.

Instruction

1. Make a note of the original cubic equation in the form: x3+a*x2+b*x+c=0. To do this, all the coefficients of the equation divide by the first coefficient with a multiplier of x3 so that it became equal to one.
2. Based on the algorithm of the method of vieta, cardan, calculate the values of R and Q according to the respective formulae: Q =(a2-3b)/9, R=(2a3-9ab+27c)/54. Moreover, the coefficients a, b and C are the coefficients of the given equation.
3. Compare the obtained values of R and Q. If it is the expression Q3 >R2 , therefore, in the initial equation there are 3 real roots. Calculate them by the formulas of vieta.
   
4. When Q3 values <= R2 , the solution is one real root x1 and two complex conjugate roots. To define them we need to find intermediate values A and B. Calculate their formulas Cardano.
   
5. Find the first valid root by the formula x1=(B + A) a/3. For different values of A and b define the complex conjugate roots of the cubic equation by appropriate formulas.
   
6. If the values of A and b was equal, conjugate roots, degenerate in the second real root of the original equation. This is the case when a valid root turns two. Calculate second real root by the formula x2=-A-A/3.