Solve using the Quadratic Formula
\[
x^{2}-2 x-15=0
\]

Step 1 ：We are given the quadratic equation \(x^{2}-2 x-15=0\).

Step 2 ：The quadratic formula is used to solve equations of the form \(ax^2 + bx + c = 0\). The formula is given by: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\).

Step 3 ：In this case, \(a = 1\), \(b = -2\), and \(c = -15\). We can substitute these values into the quadratic formula to find the solutions for \(x\).

Step 4 ：First, we calculate the discriminant \(D = b^2 - 4ac = 64\).

Step 5 ：Then, we substitute \(a\), \(b\), and \(D\) into the quadratic formula to find the solutions for \(x\).

Step 6 ：The solutions are \(x1 = 5.0\) and \(x2 = -3.0\).

Step 7 ：Final Answer: The solutions to the equation \(x^{2}-2 x-15=0\) are \(x = \boxed{5.0}\) and \(x = \boxed{-3.0}\).