/*
 * Code MBMK-1
 * Arduino Muhammad ibn Musa al-Khwarizmi Solver also called Quadratic
 * This program solves real and imaginary roots of 2nd degree polynomials
 * 
 * Muhammad ibn Musa al-Khwarizmi was a Persian mathematician from Greater Khorasan in from 820 AD
 * Greater Khorasan is currently Afghanistan, Uzbekistan, Turkmenistan, eastern Iran and Tajikistan
 * 
 * https://en.wikipedia.org/wiki/Muhammad_ibn_Musa_al-Khwarizmi
 * 
 * written by Ahmad Shamshiri www.robojax.com, https://www.youtube.com/@robojax
 * written on Mar 09, 2023
 * 
 * Main idea taken from 
 * https://www.programiz.com/cpp-programming/examples/quadratic-roots
 */
float a=4;//value of "a"
float b=1.3;//value of "b"
float c=2;//value of "c"

float x1, x2, discriminant, realPart, imaginaryPart;

void setup() {
  Serial.begin(9600);
  Serial.println("================================");
  Serial.println("Muhammad ibn Musa al-Khwarizmi 2nd Degree Solver");
  discriminant = b*b - 4*a*c;
   if (discriminant > 0) {
        x1 = (-b + sqrt(discriminant)) / (2*a);
        x2 = (-b - sqrt(discriminant)) / (2*a);
        Serial.println( "Roots are real and different.");
        Serial.print( "x1 = ");
        Serial.println(x1);
        Serial.print("x2 = ");
        Serial.println(x2);
    }else if(discriminant == 0){
        Serial.println( "Roots are real and same.");
        x1 = -b/(2*a);
        Serial.print( "x1 = x2 =  ");
        Serial.println(x1);
    }else{
        realPart = -b/(2*a);
        imaginaryPart =sqrt(-discriminant)/(2*a);
       Serial.println("Roots are complex and different." );
       Serial.print("x1 = ");
       Serial.print(realPart);
       Serial.print("+");
       Serial.print(imaginaryPart);
       Serial.println("i");

       Serial.print("x2 = ");
       Serial.print(realPart);
       Serial.print("+");
       Serial.print(imaginaryPart);
       Serial.println("i");       
          
    }

}

void loop() {
  // put your main code here, to run repeatedly:

}