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### Find the roots for the following equation $$x^2 - 8x + 5 = 0$$

$$x = 4+\sqrt{11}$$ or $$x = 4-\sqrt{11}$$
$$x = 2+\sqrt{11}$$ or $$x = 2-\sqrt{11}$$
$$x = 3+\sqrt{11}$$ or $$x = 3-\sqrt{11}$$
$$x = 5+\sqrt{11}$$ or $$x = 5-\sqrt{11}$$

### Find the roots for the following equation $$4x^2 + 8x - 9 = 0$$

$$x = -1+\frac{\sqrt{11}}{2}$$ or $$x = -1-\frac{\sqrt{11}}{2}$$
$$x = -3+\frac{\sqrt{13}}{2}$$ or $$x = 31-\frac{\sqrt{13}}{2}$$
$$x = -2+\frac{\sqrt{13}}{2}$$ or $$x = -2-\frac{\sqrt{13}}{2}$$
$$x = -1+\frac{\sqrt{13}}{2}$$ or $$x = -1-\frac{\sqrt{13}}{2}$$

### Find the roots for the following equation $$3x^2 - 12x - 7 = 0$$

$$x = 2+\frac{\sqrt{57}}{3}$$ or $$x = 2-\frac{\sqrt{57}}{3}$$
$$x = 3+\frac{\sqrt{57}}{3}$$ or $$x = 3-\frac{\sqrt{57}}{3}$$
$$x = 2+\frac{\sqrt{51}}{3}$$ or $$x = 2-\frac{\sqrt{51}}{3}$$
$$x = 4+\frac{\sqrt{57}}{3}$$ or $$x = 4-\frac{\sqrt{57}}{3}$$

### Find the roots for the following equation $$20x^2 - 13x + 2 = 0$$

$$x = -\frac{1}{2}$$ or $$x = \frac{1}{4}$$
$$x = -\frac{5}{2}$$ or $$x = \frac{1}{4}$$
$$x = -\frac{5}{2}$$ or $$x = \frac{3}{4}$$
$$x = -\frac{7}{2}$$ or $$x = \frac{1}{4}$$

### Find the roots for the following equation $$8x^2 + 14x - 15 = 0$$

$$x = -\frac{5}{2}$$ or $$x = \frac{3}{4}$$
$$x = -\frac{3}{2}$$ or $$x = \frac{3}{4}$$
$$x = -\frac{5}{2}$$ or $$x = \frac{1}{4}$$
$$x = -\frac{5}{2}$$ or $$x = \frac{5}{4}$$

### Find the roots for the following equation $$\frac{3}{x}- \frac{11}{2}=5x$$

$$x = -\frac{1}{2}$$ or $$x = \frac{1}{5}$$
$$x = -\frac{3}{2}$$ or $$x = \frac{1}{5}$$
$$x = -\frac{3}{2}$$ or $$x = \frac{2}{5}$$
$$x = -\frac{1}{2}$$ or $$x = \frac{2}{5}$$

### Find the roots for the following equation $$6x^2 - x - 15 = 0$$

$$x = -\frac{3}{2}$$ or $$x = \frac{5}{3}$$
$$x = -\frac{1}{2}$$ or $$x = \frac{5}{3}$$
$$x = -\frac{3}{2}$$ or $$x = \frac{7}{3}$$
$$x = \frac{3}{2}$$ or $$x = \frac{5}{3}$$

### Find the roots for the following equation $$8x^2 + 10x - 25 = 0$$

$$x = -\frac{5}{2}$$ or $$x = -\frac{1}{4}$$
$$x = -\frac{5}{2}$$ or $$x = \frac{3}{4}$$
$$x = -\frac{5}{2}$$ or $$x = \frac{1}{4}$$
$$x = -\frac{1}{2}$$ or $$x = \frac{1}{4}$$

### Find the roots for the following equation $$20x^2 - 13x + 2 = 0$$

$$x = \frac{5}{4}$$ or $$x = -\frac{5}{2}$$
$$x = \frac{1}{4}$$ or $$x = -\frac{1}{2}$$
$$x = \frac{5}{4}$$ or $$x = -\frac{3}{2}$$
$$x = \frac{1}{4}$$ or $$x = -\frac{5}{2}$$

### Find the roots for the following equation $$\frac{2x-7}{7}=\frac{6}{3x-1}$$

$$x = 1$$ or $$x = -\frac{7}{6}$$
$$x = 5$$ or $$x = -\frac{5}{6}$$
$$x = 5$$ or $$x = -\frac{1}{6}$$
$$x = 5$$ or $$x = -\frac{7}{6}$$