1) 4 = 20x - 25x²

25x² - 20x + 4 = 0

D = 400 - 4 · 25 · 4 = 0

x = 20 / 50 = 2/5

2) 2x = x²

x² - 2x = 0

D = 4 - 4 · 1 · 0 = 4

x₁ = 2 + √4 / 2 = 2 + 2 / 2 = 2

x₂ = 2 - √4 / 2 = 2 - 2 / 2 = 0

3) 21x + 9x² + 10 = 0

9x² + 21x + 10 = 0

D = 441 - 4 · 9 · 10 = 81

x₁ = -21 + √81 / 18 = -12 / 18 = - 6 / 9

x₂ = -21 - √81 / 18 = -30 / 18 = - 15 / 9

4) 4x² = 36

4x² - 36 = 0

D = 0 - 4 · 4 · (-36) = 576

x₁ = 0 + √576 / 8 = 24 / 8 = 3

x₂ = 0 - √576 / 8 = -24 / 8 = -3

5) 5 + 4x + x² = 0

x² + 4x + 5 = 0

D = 16 - 4 · 1 · 5 = -4<0

корней нет

6) x² - 12x + 32 = 0

D = 144 - 4 · 1 · 32 = 16

x₁ = 12 + √16 / 2 = 16 / 2 = 8

x₂ = 12 - √16 / 2 = 8 / 2 = 4

7) 5 - 3a² - 2a = 0

-3a² - 2a + 5 = 0

3a² + 2a - 5 = 0

D = 4 - 4 · 3 · (-5) = 64

a₁ = -2 + √64 / 6 = 6 / 6 = 1

a₂ = -2 - √64 / 6 = -10 / 6 = -5 / 3