A, (2x^2+6x+1) - (3x^2+3x+9)=-5x^2+3x-8

Let's simplify the expression \((2x^2 + 6x + 1) - (3x^2 + 3x + 9)\).

Starting with the expression:

\[
(2x^2 + 6x + 1) - (3x^2 + 3x + 9)
\]

We can distribute the minus sign across the second polynomial:

\[
= 2x^2 + 6x + 1 - 3x^2 - 3x - 9
\]

Now, combine like terms:

1. **For the \(x^2\) terms:**
\[
2x^2 - 3x^2 = -x^2
\]

2. **For the \(x\) terms:**
\[
6x - 3x = 3x
\]

3. **For the constant terms:**
\[
1 - 9 = -8
\]

Putting it all together, we have:

\[
-x^2 + 3x - 8
\]

Now, we can match this result to the options given:

- A: \(-5x^2 + 3x - 8\) (not correct)
- B: \(x^2 + 3x + 8\) (not correct)
- C: \(-x^2 + 3x - 8\) (correct)
- D: \(5x^2 + 9x + 10\) (not correct)

The correct answer is **C**: \((2x^2 + 6x + 1) - (3x^2 + 3x + 9) = -x^2 + 3x - 8\).