#include <iostream>
#include <cmath>
#include <vector>

double computeDiscriminant(double a, double b, double c) {
     return pow(b, 2) - (4 * a * c);
}

 double applyQuadraticFormula(double a, double b, double c, int sign) {
     double numerator = -b + (sign * sqrt(computeDiscriminant(a, b, c)));
     double denominator = 2 * a;
     return numerator / denominator;
}

std::vector<double> solveQuadraticEquation( double a, double b, double c ){
    if ( a == 0.0 ) throw std::runtime_error("a must not be 0");
    std::vector<double> results;
    double discriminant = computeDiscriminant(a, b, c);
    if ( discriminant >= 0.0 ){
        results.push_back(applyQuadraticFormula(a,b,c,1) );
        if ( discriminant > 0.0){
            results.push_back(applyQuadraticFormula(a,b,c,-1) );
        }
    }
    return results;
}

double readDoubleFromCin(){
    double result;
    std::cin >> result;
    if ( std::cin.fail() ) throw std::runtime_error("could not read number from cin");
    return result;
}

int main(){
    try{
        double a, b, c;

        std::cout << "Please enter the values of a, b, and c: ";

        a = readDoubleFromCin();
        b = readDoubleFromCin();
        c = readDoubleFromCin();

        std::vector<double> solutions = solveQuadraticEquation( a, b, c );

        switch ( solutions.size() ){
            case 0:
                std::cout << "There is no solution." << std::endl;
                break;
            case 1:
                std::cout << "There is 1 solution." << std::endl;
                std::cout << "The solution is: " << solutions.at(0) << std::endl;
                break;
            case 2:
                std::cout << "There are 2 solutions." << std::endl;
                std::cout << "The solutions are: " << solutions.at(0)
                            << " and " << solutions.at(1) << std::endl;
                break;
        }
    }
    catch(std::runtime_error& e){
        std::cout << "an error happened: " << e.what() << std::endl;
    }

    return 0;
}