Х²-4х-45=0

To solve the quadratic equation \(x^2 - 4x - 45 = 0\), we can use the quadratic formula:

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

In this equation, a = 1, b = -4, and c = -45.

Plugging these values into the formula, we get:

\(x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4 * 1 * (-45)}}{2 * 1}\)

\(x = \frac{4 \pm \sqrt{16 + 180}}{2}\)

\(x = \frac{4 \pm \sqrt{196}}{2}\)

\(x = \frac{4 \pm 14}{2}\)

Now we have two possible solutions:

1. \(x = \frac{4 + 14}{2} = \frac{18}{2} = 9\)

2. \(x = \frac{4 - 14}{2} = \frac{-10}{2} = -5\)

Therefore, the solutions to the equation \(x^2 - 4x - 45 = 0\) are \(x = 9\) and \(x = -5\).