Use the quadratic formula to solve the equation.

x^2-7x-6=0

x = (7 ± √(49+24))/2 = (7±√73)/2

The quadratic formula is used to solve quadratic equations of the form ax^2 + bx + c = 0.

For the equation x^2 - 7x - 6 = 0, we have a = 1, b = -7, and c = -6.

Now, substitute these values into the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

x = (-(-7) ± √((-7)^2 - 4(1)(-6))) / (2(1))

x = (7 ± √(49 + 24)) / 2

x = (7 ± √73) / 2

Therefore, the solutions are:

x = (7 + √73) / 2, and x = (7 - √73) / 2.

To solve the equation using the quadratic formula, we need to first identify the coefficients of the quadratic equation. The quadratic equation is in the form: ax^2 + bx + c = 0.

In this case, the equation is x^2 - 7x - 6 = 0. Therefore, we can identify the coefficients as follows:
a = 1 (coefficient of x^2)
b = -7 (coefficient of x)
c = -6 (constant term)

Now that we have the coefficients, we can use the quadratic formula, which is given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values we have:

x = (-(-7) ± √((-7)^2 - 4(1)(-6))) / (2(1))

Simplifying further:

x = (7 ± √(49 + 24)) / 2

x = (7 ± √73) / 2

So the solutions to the equation x^2 - 7x - 6 = 0 are:
x = (7 + √73) / 2
x = (7 - √73) / 2