Let \(x \mathbin{\spadesuit} y = \frac{x^2}{y}\) for all x and y such that \(y\neq 0\). Find all values of a such that \(a \mathbin{\spadesuit} (a + 1) = 9\). Write your answer as a list separated by commas.
a ( a + 1) =
(a^2) / (a + 1) = 9
a^2 = 9 (a + 1)
a^2 = 9a + 9
a^2 - 9a = 9
a^2 - 9a + 81/4 = 9 + 81/4
(a + 9/2)^2 = 117/4 take both roots
a = (-9 - sqrt (117) ) / 2 and a = (-9 + sqrt (117) ) / 2
