#!/usr/bin/python3

from math import sqrt

from util.io import readvalue

def solution_count(a, b, c):
	"""
	Calculates the number of real solutions
	for a*x**2 + b*x + c = 0.

	Returns: 0 or 1 or 2

	Method:

	After doing some fiddling you can get the equation

	(x + b/(2*a))**2 = (b/(2*a))**2 - c/a

	You can derive that the equation has 
	no real solution, if (b/(2*a))**2 - c/a < 0
	one real solution, if (b/(2*a))**2 - c/a = 0,
	two real solutions, if (b/(2*a))**2 - c/a > 0.
	"""

	rterm = (b/(2*a))**2 - c/a

	if(rterm < 0):
		return 0
	if(rterm == 0):
		return 1
	if(rterm > 0):
		return 2

def solutions(a, b, c):
	"""
	Returns the solution(s) of a*x**2 + b*x + c = 0.

	If the equation has no solution, it returns None,
	a tuple of the soltions, otherwise.
	"""
	# Get the number of solutions:
	number_of_solutions = solution_count(a, b, c)

	if(not number_of_solutions):
		return


	if(number_of_solutions == 1):
		return (-b / (2*a), )
	else:
		rterm = sqrt((b/(2*a))**2 - c/a)
		return (-b / (2*a) + rterm, -b / (2*a) - rterm)



if( __name__ == "__main__"):
	print("Program to find the solution(s) for a*x**2 + b*x + c = 0")
	a = readvalue("a > ", float)
	b = readvalue("b > ", float)
	c = readvalue("c > ", float)

	number_of_solutions = solution_count(a, b, c)
	
	messages = ["There are no real solutions."
			, "There is exactly one real solution."
			, "There are exactly two real solutions."]
	print(messages[number_of_solutions])

	if(number_of_solutions == 1):
		print("The solution is:", solutions(a, b, c)[0])
	if(number_of_solutions == 2):
		print("The first solution is:", solutions(a, b, c)[0])
		print("The second solution is:", solutions(a, b, c)[1])