To solve the equation
\[ \sqrt{3x + 12} = 9, \]
we start by squaring both sides to eliminate the square root:
\[ (\sqrt{3x + 12})^2 = 9^2. \]
This simplifies to:
\[ 3x + 12 = 81. \]
Next, we solve for \(x\) by isolating it. First, subtract 12 from both sides:
\[ 3x = 81 - 12, \]
which simplifies to:
\[ 3x = 69. \]
Now, divide both sides by 3:
\[ x = \frac{69}{3} = 23. \]
Now, let's check if this solution is extraneous by substituting \(x = 23\) back into the original equation:
Calculate \(3x + 12\) when \(x = 23\):
\[ 3(23) + 12 = 69 + 12 = 81. \]
Now, take the square root:
\[ \sqrt{81} = 9. \]
Since the left side equals the right side of the original equation, we confirm:
\[ \sqrt{3x + 12} = 9. \]
Thus, the solution \(x = 23\) is valid and not extraneous.
So, the final solution is:
\[ \boxed{23}. \]