Решите уравнения: 1. 5x² - 8x - 4 = 0; 2. x² + 6x + 5 = 0; 3. x² + 3x = 10; 4. -3x² - 10x + 8 = 0; 5. x² + 3x + 4 = 0; 6. 4x² - 4x + 1 = 0

**Ответы:** 1. $x_{1}=2, x_{2}=-0,4$ 2. $x_{1}=-1, x_{2}=-5$ 3. $x_{1}=2, x_{2}=-5$ 4. $x_{1}=-4, x_{2}=\frac{2}{3}$ 5. Корней нет 6. $x=0,5$ **Решение:** 1. $5x^2 - 8x - 4 = 0$ $D = (-8)^2 - 4 \cdot 5 \cdot (-4) = 64 + 80 = 144 = 12^2$ $x_1 = \frac{8 + 12}{2 \cdot 5} = \frac{20}{10} = 2$ $x_2 = \frac{8 - 12}{10} = -0,4$ 2. $x^2 + 6x + 5 = 0$ $D = 6^2 - 4 \cdot 1 \cdot 5 = 36 - 20 = 16 = 4^2$ $x_1 = \frac{-6 + 4}{2} = -1$ $x_2 = \frac{-6 - 4}{2} = -5$ 3. $x^2 + 3x - 10 = 0$ $D = 3^2 - 4 \cdot 1 \cdot (-10) = 9 + 40 = 49 = 7^2$ $x_1 = \frac{-3 + 7}{2} = 2$ $x_2 = \frac{-3 - 7}{2} = -5$ 4. $-3x^2 - 10x + 8 = 0$ (умножим на $-1$: $3x^2 + 10x - 8 = 0$) $D = 10^2 - 4 \cdot 3 \cdot (-8) = 100 + 96 = 196 = 14^2$ $x_1 = \frac{-10 + 14}{6} = \frac{4}{6} = \frac{2}{3}$ $x_2 = \frac{-10 - 14}{6} = -4$ 5. $x^2 + 3x + 4 = 0$ $D = 3^2 - 4 \cdot 1 \cdot 4 = 9 - 16 = -7$ Так как $D < 0$, корней нет. 6. $4x^2 - 4x + 1 = 0$ $D = (-4)^2 - 4 \cdot 4 \cdot 1 = 16 - 16 = 0$ $x = \frac{4}{2 \cdot 4} = 0,5$