def tau(x, alpha):
    return (0.5 * ((x - (1 + alpha)) + np.sqrt((((x - (1 + alpha)) ** 2) - (4 * alpha)))))
def tau(x, alpha):
    return (0.5 * ((x - (1 + alpha)) + np.sqrt((((x - (1 + alpha)) ** 2) - (4 * alpha)))))