f(x) = f(f(x)) + 16x + 5
x^2 - 3x + 1 = [ x^2 - 3x + 1]^2 -3[ x^2 - 3x + 1] + 1 + 16x + 5
x^2 - 3x + 1 = x^4 - 6 x^3 + 11 x^2 - 6 x + 1 -3x^2 + 9x - 3 + 1 + 16x + 5
x^4 -6x^3 + 7x^2+ 22x -3 = 0
By graph, the solutions for x are
x ≈ -1.2305
x ≈ -0.14377