Solve the equation for $x$ : \[ x^{2}+17 x+60=0 \]

Step 1 ：Given the quadratic equation: \(x^2 + 17x + 60 = 0\)

Step 2 ：Using the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\) with \(a = 1\), \(b = 17\), and \(c = 60\)

Step 3 ：Calculate the discriminant: \(\Delta = b^2 - 4ac = 49\)

Step 4 ：Find the two solutions: \(x_1 = \frac{-17 + \sqrt{49}}{2} = -5\) and \(x_2 = \frac{-17 - \sqrt{49}}{2} = -12\)

Step 5 ：\(\boxed{x = -5, -12}\)