Without rotating the original coordinate axes, to which point should origin be transferred, so that the equation `x^2 + y^2-4x + 6y-7=0` is changed to an equation which contains no term of first degree?

Explanation

To solve the problem, we need to find the point to which the origin should be transferred so that the given equation \(x^2 + y^2 - 4x + 6y - 7 = 0\) contains no first-degree terms.

### Step-by-Step Solution:

1. **Rewrite the given equation**:
Start with the original equation:
\[ x^2 + y^2 - 4x + 6y - 7 = 0 \]
Rearranging gives:
\[ x^2 - 4x + y^2 + 6y = 7 \]

2. **Complete the square for the x-terms**:
For the \(x\) terms \(x^2 - 4x\):
\[ x^2 - 4x = (x - 2)^2 - 4 \]

3. **Complete the square for the y-terms**:
For the \(y\) terms \(y^2 + 6y\):
\[ y^2 + 6y = (y + 3)^2 - 9 \]

4. **Substitute back into the equation**:
Substitute the completed squares back into the equation:
\[ (x - 2)^2 - 4 + (y + 3)^2 - 9 = 7 \]
Simplifying this gives:
\[ (x - 2)^2 + (y + 3)^2 - 13 = 7 \]
\[ (x - 2)^2 + (y + 3)^2 = 20 \]

5. **Identify the new center of the circle**:
The equation \((x - 2)^2 + (y + 3)^2 = 20\) represents a circle with center at the point \((2, -3)\).

6. **Determine the new origin**:
To eliminate the first-degree terms, we need to shift the origin to the center of the circle, which is at the point \((2, -3)\).

### Conclusion:
Thus, the origin should be transferred to the point \((2, -3)\).