28.15 a) 2x² + 10x + 12 = 0; 6) -3x²+18x - 24 = 0;

а) 2x² + 10x + 12 = 0

a = 2, b = 10, c = 12

$$D = b^2 - 4ac = 10^2 - 4 \cdot 2 \cdot 12 = 100 - 96 = 4$$

$$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{-10 + \sqrt{4}}{2 \cdot 2} = \frac{-10 + 2}{4} = \frac{-8}{4} = -2$$

$$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{-10 - \sqrt{4}}{2 \cdot 2} = \frac{-10 - 2}{4} = \frac{-12}{4} = -3$$

б) -3x² + 18x - 24 = 0

a = -3, b = 18, c = -24

$$D = b^2 - 4ac = 18^2 - 4 \cdot (-3) \cdot (-24) = 324 - 288 = 36$$

$$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{-18 + \sqrt{36}}{2 \cdot (-3)} = \frac{-18 + 6}{-6} = \frac{-12}{-6} = 2$$

$$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{-18 - \sqrt{36}}{2 \cdot (-3)} = \frac{-18 - 6}{-6} = \frac{-24}{-6} = 4$$

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