return solution(s) for x, to the quadratic equation a*x^2 + b*x + c
    when it equals zero using the quadratic formula

def quadraticSolver(a, b, c):
    """return solution(s) for x, to the quadratic equation a*x^2 + b*x + c
    when it equals zero using the quadratic formula"""
    if a == 0:
        if b == 0:  return [] # attempting to solve an equation with infinite (0=0) or impossible (0=3) solutions for x
        else:       return [-c / float(b)]
    else:
        d = b**2.0 - 4*a*c # calculate the discriminant
        if d < 0:   return [] # would require math.sqrt a negative number, yielding a complex number
        solvedPart0 = 1/(2.0*a)
        solvedPart1 = -b * solvedPart0
        if d == 0:  return [ solvedPart1 ] # two values at same 'x'
        else: # i.e. d > 0   apply full quadratic formula
            solvedPart2 = math.sqrt(d)*solvedPart0
            return [ solvedPart1+solvedPart2, solvedPart1-solvedPart2 ]