А) 3х^2 +6х-105>0

To solve the inequality 3x^2 + 6x - 105 > 0, we can follow these steps:

1. Factorize the quadratic expression: 3x^2 + 6x - 105 = 3(x^2 + 2x - 35) = 3(x + 7)(x - 5).

2. Set each factor equal to zero to find the critical points: x + 7 = 0 => x = -7 x - 5 = 0 => x = 5

3. Create a number line and plot the critical points on it: -∞ ---[ -7 ]---[ 5 ]--- +∞

4. Choose a test point from each interval and determine if the inequality holds true. Let's choose x = -8, x = 0, and x = 6.

   For x = -8: 3(-8 + 7)(-8 - 5) = 3(-1)(-13) = 39 > 0

   For x = 0: 3(0 + 7)(0 - 5) = 3(7)(-5) = -105 < 0

   For x = 6: 3(6 + 7)(6 - 5) = 3(13)(1) = 39 > 0

5. Determine the solution based on the test points: The inequality holds true for the interval (-∞, -7) and (5, +∞).

Therefore, the solution to the inequality 3x^2 + 6x - 105 > 0 is: x < -7 or x > 5.