3x² - 10x - 8 < 0
3x² - 10x - 8 = 0 D = b²-4ac = 100+96 = 196 = 14²
x₁ = (-b+√D)/2a = (10+14)/6 = 4
x₂ = (-b -√D)/2a = (10-14)/6 = -2/3
3x² - 10x - 8 = 3(x - 4)(x + 2/3) = (x - 4)(3x + 2)
(x - 4)(3x + 2) < 0
{ x - 4 < 0 { x - 4 > 0
{ 3x + 2 > 0 { 3x + 2 < 0
{ x < 4 { x > 4
{ x > -2/3 { x < -2/3
(-2/3; 4) ∅
Ответ: (-2/3; 4)