#!/usr/bin/env python
import math

class Quadratic(object):
    def __init__(self, a, b, c):
        self._a, self._b, self._c = a, b, c
        for i in (a, b, c):
            if type(i) is not int:
                raise TypeError, "Only ints please."
       
    def solve(self):
        '''Applies the quadratic formula to the given
coefficients plugged into a quadratic equation'''
        x = self._b**2-4*self._a*self._c
        if x < 0:
            return None # There's no real solution to this equation
        
        x = math.sqrt(x)
        return set((((-self._b+x)/2*self._a), ((-self._b-x)/2*self._a)))
        
    def __str__(self):
        '''Very sloppy way of displaying a quadratic
equation given the coefficients'''
        return '%sx^2%s%dx%s%d' % (self._a if self._a > 1 or self._a < -1 else ('-' if self._a == -1 else ''), 
                                       '+' if self._b > 0 else '',
                                       self._b,
                                       '+' if self._c > 0 else '',
                                       self._c)

if __name__ == '__main__':
    q = Quadratic(1, 2, -8)
    print q
    print q.solve()