Verified answer

5 - 14x - 3x² - 1/(3x² + 14x - 5) ≥ 2

3x² + 14x - 5 = t

-t - 1/t ≥ 2

(t² + 2t + 1)/t ≤ 0

(t + 1)²/t ≤ 0

t = -1

3x² + 14x - 5 = -1

3x² + 14x - 4 = 0

D = 14² + 4*4*3 = 196 + 48 = 244

корни иррациональные

1/t < 0

3x² + 14x - 5 < 0

D = 14² + 4*3*5 = 196 + 60 = 256

x12 = (-14 +- 16)/6 = -5  1/3

(x + 5)(3x - 1) < 0

++++++++(-5) ------------ (1/3) ++++++++

x ∈ (-5, 1/3)

целые  решения -4 -3 -2 -1 0

Сумма -4 - 3 - 2 - 1 + 0 = -10