Решите квадратные уравнения: 11) 3x²-7x+4=0; 12) 2x²-x+15=0; 13) 8x²-6x+1=0; 14) 4x²-3x-1=0; 15) -5x²-x+4=0; 16) 9x²+6x+1=0; 17) x²-5x+4=0; 18) 2x²+3x-2=0; 19) 2x²-5x+2=0; 20) 5x²+2x-1=0; 21) x²-x-12=0; 22) -x²-6x+7=0.

Для решения квадратных уравнений вида $ax^2 + bx + c = 0$ используем формулу дискриминанта $D = b^2 - 4ac$ и корней $x = \frac{-b \pm \sqrt{D}}{2a}$. 11) $3x^2 - 7x + 4 = 0$ $D = (-7)^2 - 4 \cdot 3 \cdot 4 = 49 - 48 = 1$ $x_1 = \frac{7+1}{6} = \frac{8}{6} = 1\frac{1}{3}; x_2 = \frac{7-1}{6} = 1$ 12) $2x^2 - x + 15 = 0$ $D = (-1)^2 - 4 \cdot 2 \cdot 15 = 1 - 120 = -119$ $D < 0$, корней нет. 13) $8x^2 - 6x + 1 = 0$ $D = (-6)^2 - 4 \cdot 8 \cdot 1 = 36 - 32 = 4$ $x_1 = \frac{6+2}{16} = \frac{8}{16} = 0,5; x_2 = \frac{6-2}{16} = \frac{4}{16} = 0,25$ 14) $4x^2 - 3x - 1 = 0$ $D = (-3)^2 - 4 \cdot 4 \cdot (-1) = 9 + 16 = 25$ $x_1 = \frac{3+5}{8} = 1; x_2 = \frac{3-5}{8} = -0,25$ 15) $-5x^2 - x + 4 = 0$ (умножим на $-1$: $5x^2 + x - 4 = 0$) $D = 1^2 - 4 \cdot 5 \cdot (-4) = 1 + 80 = 81$ $x_1 = \frac{-1+9}{10} = 0,8; x_2 = \frac{-1-9}{10} = -1$ 16) $9x^2 + 6x + 1 = 0$ $D = 6^2 - 4 \cdot 9 \cdot 1 = 36 - 36 = 0$ $x = \frac{-6}{18} = -\frac{1}{3}$ 17) $x^2 - 5x + 4 = 0$ $D = (-5)^2 - 4 \cdot 1 \cdot 4 = 25 - 16 = 9$ $x_1 = \frac{5+3}{2} = 4; x_2 = \frac{5-3}{2} = 1$ 18) $2x^2 + 3x - 2 = 0$ $D = 3^2 - 4 \cdot 2 \cdot (-2) = 9 + 16 = 25$ $x_1 = \frac{-3+5}{4} = 0,5; x_2 = \frac{-3-5}{4} = -2$ 19) $2x^2 - 5x + 2 = 0$ $D = (-5)^2 - 4 \cdot 2 \cdot 2 = 25 - 16 = 9$ $x_1 = \frac{5+3}{4} = 2; x_2 = \frac{5-3}{4} = 0,5$ 20) $5x^2 + 2x - 1 = 0$ $D = 2^2 - 4 \cdot 5 \cdot (-1) = 4 + 20 = 24$ $x_{1,2} = \frac{-2 \pm \sqrt{24}}{10} = \frac{-2 \pm 2\sqrt{6}}{10} = \frac{-1 \pm \sqrt{6}}{5}$ 21) $x^2 - x - 12 = 0$ $D = (-1)^2 - 4 \cdot 1 \cdot (-12) = 1 + 48 = 49$ $x_1 = \frac{1+7}{2} = 4; x_2 = \frac{1-7}{2} = -3$ 22) $-x^2 - 6x + 7 = 0$ (умножим на $-1$: $x^2 + 6x - 7 = 0$) $D = 6^2 - 4 \cdot 1 \cdot (-7) = 36 + 28 = 64$ $x_1 = \frac{-6+8}{2} = 1; x_2 = \frac{-6-8}{2} = -7$