Question 109
The first, seventh, and seventeenth terms of an arithmetic progression are distinct and consecutive terms of a geometric progression. Find the common difference of the arithmetic progression if its first term is a solution of the equation
$$
x^2 - 9x + x\sqrt{12-x} - 9\sqrt{12-x} = 0.
$$
$$
x^2 - 9x + x\sqrt{12-x} - 9\sqrt{12-x} = 0.
$$