28.18 a) 6x(2x+1) = 5x + 1; 6) 2x(x - 8) = -x - 18;

а) 6x(2x+1) = 5x + 1

12x² + 6x = 5x + 1

12x² + x - 1 = 0

a = 12, b = 1, c = -1

$$D = b^2 - 4ac = 1^2 - 4 \cdot 12 \cdot (-1) = 1 + 48 = 49$$

$$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{-1 + \sqrt{49}}{2 \cdot 12} = \frac{-1 + 7}{24} = \frac{6}{24} = \frac{1}{4}$$

$$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{-1 - \sqrt{49}}{2 \cdot 12} = \frac{-1 - 7}{24} = \frac{-8}{24} = -\frac{1}{3}$$

б) 2x(x - 8) = -x - 18

2x² - 16x = -x - 18

2x² - 15x + 18 = 0

a = 2, b = -15, c = 18

$$D = b^2 - 4ac = (-15)^2 - 4 \cdot 2 \cdot 18 = 225 - 144 = 81$$

$$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{15 + \sqrt{81}}{2 \cdot 2} = \frac{15 + 9}{4} = \frac{24}{4} = 6$$

$$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{15 - \sqrt{81}}{2 \cdot 2} = \frac{15 - 9}{4} = \frac{6}{4} = \frac{3}{2}$$

Ответ: a) x₁ = 1/4, x₂ = -1/3; б) x₁ = 6, x₂ = 3/2