#include <array>
#include <complex>
#include <utility>
#include <vector>
#include <math.h>
#include <limits>
#include <iostream>


namespace Equations {

template<typename t>
std::pair<bool, std::vector<std::complex<t> > > quadratic(std::array< std::complex<t>, 3> arr)
{

    std::pair<bool, std::vector<std::complex<t> > > p;
    if (std::norm(arr[2]) < std::numeric_limits<t>::epsilon() &&
        std::norm(arr[1]) < std::numeric_limits<t>::epsilon() &&
        std::norm(arr[0]) < std::numeric_limits<t>::epsilon()) {
        std::vector<std::complex<t> > v;
        p.second = v;
        p.first = false;
    } else if (std::norm(arr[2]) < std::numeric_limits<t>::epsilon() &&
                std::norm(arr[1]) < std::numeric_limits<t>::epsilon() &&
                std::norm(arr[0]) >= std::numeric_limits<t>::epsilon()) {
        std::vector<std::complex<t> > v;
        p.second = v;
        p.first = true;
    } else if (std::norm(arr[2]) < std::numeric_limits<t>::epsilon() &&
                std::norm(arr[1]) > std::numeric_limits<t>::epsilon()) {
        std::vector<std::complex<t> > v = {-arr[0]/arr[1]};
        p.first = true;
        p.second = v;
    } else {
        std::vector<std::complex<t> > v;
        std::complex<t> d = arr[1] * arr[1] - std::complex<t>(4) * arr[2] * arr[0];
        v.push_back((-arr[1] - std::sqrt(d))/(std::complex<t>(2) * arr[2]));
        v.push_back((-arr[1] + std::sqrt(d))/(std::complex<t>(2) * arr[2]));

        p.first = true;
        p.second = v;
    }

    return p;
}

}