x^2-5x-6=0

To solve the quadratic equation \( x^2 - 5x - 6 = 0 \), we can factor it or use the quadratic formula. Let's first try factoring.

We are looking for two numbers that multiply to \(-6\) (the constant term) and add to \(-5\) (the coefficient of the linear term). The numbers \(-6\) and \(1\) fit this requirement:

\[ x^2 - 6x + 1x - 6 = 0 \]

Now we can factor by grouping:

\[ (x - 6)(x + 1) = 0 \]

Setting each factor equal to zero gives us the solutions:

1. \( x - 6 = 0 \) ⟹ \( x = 6 \)
2. \( x + 1 = 0 \) ⟹ \( x = -1 \)

Thus, the solutions to the equation \( x^2 - 5x - 6 = 0 \) are:

\[ x = 6 \quad \text{and} \quad x = -1 \]