The vertex of an equilateral triangle is `(2,3)` and the equation of the opposite side is `x+y=2`. Then, the other two sides are `y-3=(2pmsqrt3)(x-2)`.

Explanation

To solve the problem, we need to find the equations of the other two sides of the equilateral triangle given one vertex and the equation of the opposite side.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Vertex of the equilateral triangle: \( A(2, 3) \)
- Equation of the opposite side: \( x + y = 2 \)

2. **Find the Slope of the Opposite Side:**
- The equation \( x + y = 2 \) can be rewritten in slope-intercept form \( y = -x + 2 \).
- The slope \( m_1 \) of this line is \( -1 \).

3. **Determine the Angle Between the Sides:**
- In an equilateral triangle, the angle between any two sides is \( 60^\circ \).
- The tangent of the angle \( \theta \) between the two lines can be given by the formula:
\[ \tan(\theta) = \frac{m_2 - m_1}{1 + m_1 m_2} \]
- For \( \theta = 60^\circ \), we have \( \tan(60^\circ) = \sqrt{3} \).

4. **Set Up the Equation:**
- Let \( m_2 \) be the slope of one of the sides we need to find.
- Using the slopes, we can set up two equations based on the tangent formula:
\[ \sqrt{3} = \frac{m_2 + 1}{1 - m_2} \quad \text{(1)} \]
\[ -\sqrt{3} = \frac{m_2 + 1}{1 - m_2} \quad \text{(2)} \]

5. **Solve Equation (1):**
- Cross-multiply to solve for \( m_2 \):
\[ \sqrt{3}(1 - m_2) = m_2 + 1 \]
\[ \sqrt{3} - \sqrt{3}m_2 = m_2 + 1 \]
\[ \sqrt{3} - 1 = m_2 + \sqrt{3}m_2 \]
\[ m_2(1 + \sqrt{3}) = \sqrt{3} - 1 \]
\[ m_2 = \frac{\sqrt{3} - 1}{1 + \sqrt{3}} \]

6. **Solve Equation (2):**
- Similarly, for equation (2):
\[ -\sqrt{3}(1 - m_2) = m_2 + 1 \]
\[ -\sqrt{3} + \sqrt{3}m_2 = m_2 + 1 \]
\[ \sqrt{3}m_2 - m_2 = \sqrt{3} + 1 \]
\[ m_2(\sqrt{3} - 1) = \sqrt{3} + 1 \]
\[ m_2 = \frac{\sqrt{3} + 1}{\sqrt{3} - 1} \]

7. **Write the Equations of the Lines:**
- Using point-slope form \( y - y_1 = m(x - x_1) \) for both slopes:
- For \( m_2 = \frac{\sqrt{3} - 1}{1 + \sqrt{3}} \):
\[ y - 3 = \left(\frac{\sqrt{3} - 1}{1 + \sqrt{3}}\right)(x - 2) \]
- For \( m_2 = \frac{\sqrt{3} + 1}{\sqrt{3} - 1} \):
\[ y - 3 = \left(\frac{\sqrt{3} + 1}{\sqrt{3} - 1}\right)(x - 2) \]

### Final Result:
The equations of the other two sides of the equilateral triangle are:
1. \( y - 3 = (2 + \sqrt{3})(x - 2) \)
2. \( y - 3 = (2 - \sqrt{3})(x - 2) \)