Решить уравнения, обязательно с помощью Дискриминанта.

Решение:

1. \( 0,5x^2 = 0 \)
   \( x^2 = 0 \)
   \( x = 0 \)
2. \( x^2 - 9 = 0 \)
   \( x^2 = 9 \)
   \( x = ±3 \)
3. \( 2x^2 + 15 = 0 \)
   \( 2x^2 = -15 \)
   \( x^2 = -7,5 \)
   Корней нет.
4. \( x^2 - 12x + 36 = 0 \)
   \( D = (-12)^2 - 4 · 1 · 36 = 144 - 144 = 0 \)
   \( x = \frac{12}{2} = 6 \)
5. \( 3x^2 + 2x = 0 \)
   \( x(3x+2) = 0 \)
   \( x = 0 \) или \( 3x+2 = 0 \) \( x = -2/3 \)
6. \( 2x^2 - 16 = 0 \)
   \( 2x^2 = 16 \)
   \( x^2 = 8 \)
   \( x = ±√8 = ±2√2 \)
7. \( 5(x^2 + 2) = 2(x^2 + 5) \)
   \( 5x^2 + 10 = 2x^2 + 10 \)
   \( 3x^2 = 0 \)
   \( x^2 = 0 \)
   \( x = 0 \)
8. \( (x + 1)^2 - 4 = 0 \)
   \( (x + 1)^2 = 4 \)
   \( x + 1 = ±2 \)
   \( x = -1 ±2 \)
   \( x_1 = 1 \), \( x_2 = -3 \)
9. \( -1,5x^2 = 0 \)
   \( x^2 = 0 \)
   \( x = 0 \)
10. \( x^2 - 4 = 0 \)
    \( x^2 = 4 \)
    \( x = ±2 \)
11. \( x^2 - 3x - 5 = 11 - 3x \)
    \( x^2 - 5 = 11 \)
    \( x^2 = 16 \)
    \( x = ±4 \)
12. \( 5x^2 - 6 = 15x - 6 \)
    \( 5x^2 = 15x \)
    \( 5x^2 - 15x = 0 \)
    \( 5x(x-3) = 0 \)
    \( x = 0 \) или \( x = 3 \)
13. \( x^2 + 2x - 3 = 2x + 6 \)
    \( x^2 - 3 = 6 \)
    \( x^2 = 9 \)
    \( x = ±3 \)
14. \( 2x^2 - 4x = x(6x-3) \)
    \( 2x^2 - 4x = 6x^2 - 3x \)
    \( 4x^2 + x = 0 \)
    \( x(4x+1) = 0 \)
    \( x = 0 \) или \( 4x+1 = 0 \) \( x = -1/4 \)
15. \( x^2 - 3x - 5 = 11 - 3x \)
    \( x^2 - 5 = 11 \)
    \( x^2 = 16 \)
    \( x = ±4 \)

Ответ: 1. x=0; 2. x=±3; 3. Корней нет; 4. x=6; 5. x=0, x=-2/3; 6. x=±2√2; 7. x=0; 8. x_1=1, x_2=-3; 9. x=0; 10. x=±2; 11. x=±4; 12. x=0, x=3; 13. x=±3; 14. x=0, x=-1/4; 15. x=±4.