(8) $x^{2}+7 x+10=0$

Step 1 ：Given the quadratic equation: \(x^{2}+7 x+10=0\)

Step 2 ：Using the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

Step 3 ：Substitute the coefficients: \(a = 1\), \(b = 7\), and \(c = 10\)

Step 4 ：Calculate the discriminant: \(\Delta = b^2 - 4ac = 9\)

Step 5 ：Find the two solutions: \(x_1 = \frac{-7 - \sqrt{9}}{2}\) and \(x_2 = \frac{-7 + \sqrt{9}}{2}\)

Step 6 ：\(\boxed{x_1 = -2}\), \(\boxed{x_2 = -5}\)