1. \(3x^2 - 12 = 0\) 2. \(x^2 - 5x + 6 = 0\) 3. \((x+3):2 - (2x-1):5\) 4. \((5\sqrt{3} - \sqrt{12})^2\)

Решение:

1. \(3x^2 - 12 = 0\)
   \(3x^2 = 12\)
   \(x^2 = 4\)
   \(x = \pm 2\)
2. \(x^2 - 5x + 6 = 0\)
   \(D = (-5)^2 - 4 \cdot 1 \cdot 6 = 25 - 24 = 1\)
   \(x_1 = \frac{5 + 1}{2} = 3\)
   \(x_2 = \frac{5 - 1}{2} = 2\)
3. \(\frac{x+3}{2} - \frac{2x-1}{5} = \frac{5(x+3) - 2(2x-1)}{10} = \frac{5x + 15 - 4x + 2}{10} = \frac{x+17}{10}\)
4. \((5\sqrt{3} - \sqrt{12})^2 = (5\sqrt{3} - 2\sqrt{3})^2 = (3\sqrt{3})^2 = 9 \cdot 3 = 27\)

Ответ: 1. \(x = \pm 2\); 2. \(x_1 = 3, x_2 = 2\); 3. \(\frac{x+17}{10}\); 4. \(27\).