x^2 - 4x - 5 = 0

1. Identify the coefficients:
- \( a = 1 \)
- \( b = -4 \)
- \( c = -5 \)

2. Calculate the discriminant:
b^2 - 4ac = (-4)^2 - 4 \times 1 \times (-5) = 16 + 20 = 36

3. Apply the quadratic formula:
x = \frac{-(-4) \pm \sqrt{36}}{2 \times 1}
x = \frac{4 \pm 6}{2}

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

Thus, the solutions are:
x = 5 and x = -1