The solution of the equation \(x^2 - x - 6 = 0\) is E. x = 3 or x = -2. To find the solution, we can use the quadratic formula:

\(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

where a = 1, b = -1 and c = -6. Plugging these values into the formula, we get:

\(x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4(1)(-6)}}{2(1)}\)

\(x = \frac{1 \pm \sqrt{25}}{2}\)

\(x = \frac{1 \pm 5}{2}\)

Therefore, x can be either:

\(x = \frac{1 + 5}{2} = 3\)

or

\(x = \frac{1 - 5}{2} = -2\)

These are the two possible solutions of the equation. You can check them by plugging them back into the equation and verifying that they make it true. For example, if x = 3, then:

\((3)^2 - (3) - 6 = 0\)

9 - 3 - 6 = 0

0 = 0

This is a true statement, so x = 3 is a valid solution. Similarly, you can check that x = -2 is also a valid solution.