Solve[16 x^4 - 40 a x^3 + (15 a^2 + 24 b) x^2 - 18 a b x + 3 b^2 == 0 && 5 a x - 4 x^2 - b > 0 && 15 a x - 20 x^2 - 3 b < 0 && 4 x^3 - 8 c x^2 + 5 a c x - c b < 0 && a < 0 && x < 0 && c < 0, x]