If a belongs to real number set and (1-A) / (1 + a) belongs to {a}, then a =?

If a belongs to real number set and (1-A) / (1 + a) belongs to {a}, then a =?

(1-A) / (1 + a) = a = > A ^ 2 + 2a-1 = 0 = > A = (- 2) + radical (2 ^ 2-4 * (- 1))) / 2 a = - 1 + radical 2 or a = (- 2) - radical (2 ^ 2-4 * (- 1))) / 2 a = - 1 - radical 2