Step 1 :Given the quadratic equation: \(x^{2}-14 x+24=0\)
Step 2 :Use the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)
Step 3 :Identify the coefficients: \(a = 1\), \(b = -14\), and \(c = 24\)
Step 4 :Calculate the discriminant: \(\Delta = b^2 - 4ac = 100\)
Step 5 :Find the solutions: \(x1 = \frac{-(-14) + \sqrt{100}}{2(1)} = 12\) and \(x2 = \frac{-(-14) - \sqrt{100}}{2(1)} = 2\)
Step 6 :\(\boxed{x1 = 12, x2 = 2}\)