6.
$$f ( x ) = 4 x ^ { 2 } + 12 x + 9 .$$
- Determine the number of real roots that exist for the equation \(\mathrm { f } ( x ) = 0\).
- Solve the equation \(\mathrm { f } ( x ) = 8\), giving your answers in the form \(a + b \sqrt { 2 }\) where \(a\) and \(b\) are rational.