X2-4x-5=0

To solve the quadratic equation \( x^2 - 4x - 5 = 0 \), you can use the quadratic formula:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

Here, \( a = 1 \), \( b = -4 \), and \( c = -5 \).

First, calculate the discriminant:

\[ b^2 - 4ac = (-4)^2 - 4(1)(-5) = 16 + 20 = 36 \]

Now substitute the values into the quadratic formula:

\[ x = \frac{-(-4) \pm \sqrt{36}}{2(1)} = \frac{4 \pm 6}{2} \]

This will give us two solutions:

1. \( x = \frac{4 + 6}{2} = \frac{10}{2} = 5 \)
2. \( x = \frac{4 - 6}{2} = \frac{-2}{2} = -1 \)

Therefore, the solutions to the equation \( x^2 - 4x - 5 = 0 \) are:

\[ x = 5 \quad \text{and} \quad x = -1 \]