1) x²+10x = 0 2) -x²+9=0 3) 25x² + 17 = 42x 4) x²=x+6 5) 4x²-4x+1=0 6) 9x² = 4-16x 7) 6a² + 14 = 2a

Решение:

1. \( x^2 + 10x = 0 \)
   \( x(x+10) = 0 \)
   \( x=0 \) или \( x=-10 \)
2. \( -x^2 + 9 = 0 \)
   \( x^2 = 9 \)
   \( x = \pm 3 \)
3. \( 25x^2 + 17 = 42x \)
   \( 25x^2 - 42x + 17 = 0 \)
   \( D = (-42)^2 - 4 \cdot 25 \cdot 17 = 1764 - 1700 = 64 \)
   \( x = \frac{42 \pm \sqrt{64}}{2 \cdot 25} = \frac{42 \pm 8}{50} \)
   \( x_1 = \frac{50}{50} = 1 \), \( x_2 = \frac{34}{50} = 0.68 \)
4. \( x^2 = x + 6 \)
   \( x^2 - x - 6 = 0 \)
   \( D = (-1)^2 - 4 \cdot 1 \cdot (-6) = 1 + 24 = 25 \)
   \( x = \frac{1 \pm \sqrt{25}}{2} = \frac{1 \pm 5}{2} \)
   \( x_1 = \frac{6}{2} = 3 \), \( x_2 = \frac{-4}{2} = -2 \)
5. \( 4x^2 - 4x + 1 = 0 \)
   \( D = (-4)^2 - 4 \cdot 4 \cdot 1 = 16 - 16 = 0 \)
   \( x = \frac{4}{2 \cdot 4} = \frac{4}{8} = 0.5 \)
6. \( 9x^2 = 4 - 16x \)
   \( 9x^2 + 16x - 4 = 0 \)
   \( D = 16^2 - 4 \cdot 9 \cdot (-4) = 256 + 144 = 400 \)
   \( x = \frac{-16 \pm \sqrt{400}}{2 \cdot 9} = \frac{-16 \pm 20}{18} \)
   \( x_1 = \frac{4}{18} = \frac{2}{9} \), \( x_2 = \frac{-36}{18} = -2 \)
7. \( 6a^2 + 14 = 2a \)
   \( 6a^2 - 2a + 14 = 0 \)
   \( 3a^2 - a + 7 = 0 \)
   \( D = (-1)^2 - 4 \cdot 3 \cdot 7 = 1 - 84 = -83 \)
   Действительных корней нет.

Ответ: 1) 0, -10; 2) 3, -3; 3) 1, 0.68; 4) 3, -2; 5) 0.5; 6) 2/9, -2; 7) действительных корней нет.