A very simple C program that uses the General Formula for quadratic polynomials (Ax^2 + Bx + C)

quadratic_formula.c

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

/**
 * Declare a helper boolean data type and then define 
 * some handy macros (true, false).
 *
 * Learn more about `typedef` here:
 *
 *    https://overiq.com/c-programming-101/typedef-statement-in-c/
 */
typedef unsigned char bool;

// some handy boolean constants.
#define true 1
#define false 0

/**
 * Define an enum that represents a Positive (+) and a Negative (-) sign.
 * Learn more about enums here: 
 *
 *    https://www.geeksforgeeks.org/enumeration-enum-c
 */
enum Sign {
  Positive = 1,
  Negative = -1
};

/**
 * Function declaration.
 */
float general_formula(float, float, float, enum Sign, bool*);

int main() {

    bool error;
    int a, b, c;

    printf("Introducir el valor Ax^2: ");
    scanf("%d",&a);
    printf("\nIntroducir el valor Bx: ");
    scanf("%d",&b);
    printf("\nIntroducir el valor C: ");
    scanf("%d",&c);

    float x1 = general_formula(a, b, c, Positive, &error);
    if (error) {
      printf("\nNo se puede hacer la formula general\nYa que la raiz es negativa. ");
      return 1;
    }

    float x2 = general_formula(a, b, c, Negative, &error);
    if (error) {
      printf("\nNo se puede hacer la formula general\nYa que la raiz es negativa. ");
      return 1;
    }

    printf("El primer x es: %.2f y el segundo x es: %.2f",x1,x2);

    getchar();
    return 0;
}

/**
 * The general formula of a quadratic polynomial, i.e.: of the form:
 *
 *    Ax^2 + Bx + C
 *
 * Formula:
 *
 *    x = - (b +/- sqrt(b^2 - 4ac) ) / 2a
 *
 * @param a The A coeficient.
 * @param b The B coeficient.
 * @param c The C constant.
 * @param sign That determines whether to _add_ (+) or subtract the expression sqrt(b^2 - 4ac) from b.
 * @param error A non-null pointer that will be set to `true` if the expression b^2 - 4ac is a negative
 *              number.
 *
 * @returns x1 or x2 depending on the `sign` parameter. If `error` is `true` then the return value should be ignored.
 */
float general_formula(float a, float b, float c, enum Sign sign, bool *error) {

  float sq = b * b - 4 * a * c; // b^2 - 4ac

  *error = sq < 0; // set the error, if sq is less than 0, then we have an error.

  float numerator = b + (float)(sign) * sqrt(sq); // b +/- sqrt(b^2 - 4ac)
  float denominator = 2 * a;                      // 2a

  return -(numerator / denominator);

}