To determine whether the values \(-1\) and \(73\) are solutions to the quadratic equation \(3x^2 - 4x - 4 = 3\), we first simplify the equation by moving \(3\) to the left side:
\[
3x^2 - 4x - 4 - 3 = 0
\]
This simplifies to:
\[
3x^2 - 4x - 7 = 0
\]
Now we will test both \(x = -1\) and \(x = 73\) as possible solutions by substituting them into the equation.
**Testing \(x = -1\):**
\[
3(-1)^2 - 4(-1) - 7 = 3(1) + 4 - 7 = 3 + 4 - 7 = 0
\]
So, \(x = -1\) is a solution.
**Testing \(x = 73\):**
\[
3(73)^2 - 4(73) - 7
\]
Calculating \(3(73)^2\):
\[
3(5329) = 15987
\]
Calculating \(-4(73)\):
\[
-4(73) = -292
\]
Now substituting back in:
\[
15987 - 292 - 7 = 15987 - 299 = 15688 \neq 0
\]
So, \(x = 73\) is not a solution.
Based on this evaluation, we conclude that:
**Only \(x = -1\) is a solution.**