Start with the inequality:

\(x^2 + 6x + 2 > 9\)

Simplify it:

\(x^2 + 6x + 2 - 9 > 0\)

\(x^2 + 6x - 7 > 0\)

Factor the quadratic expression:

\((x + 7)(x - 1) > 0\)

The critical points are \(x = -7\) and \(x = 1\).

Test intervals around the critical points:

1. For \(x < -7\), choose \(x = -8\):

\((-8 + 7)(-8 - 1) > 0\)

\((-1)(-9) > 0\)

\(9 > 0\) (True)

2. For \(-7 < x < 1\), choose \(x = 0\):

\((0 + 7)(0 - 1) > 0\)

\(7(-1) > 0\)

\(-7 > 0\) (False)

3. For \(x > 1\), choose \(x = 2\):

\((2 + 7)(2 - 1) > 0\)

\(9(1) > 0\)

\(9 > 0\) (True)

Thus, the solution is \(x > 1\) or \(x < -7\).