1. **State the problem:** We have a circle given by the equation $$x^2 + y^2 + x - 15 = 0$$ and one end of its diameter is at the point $(2, -3)$. We need to find the coordinates of the other end of the diameter. 2. **Rewrite the circle equation in standard form:** The general form of a circle is $$x^2 + y^2 + Dx + Ey + F = 0$$. Here, the equation is $$x^2 + y^2 + x - 15 = 0$$, which means $D=1$, $E=0$, and $F=-15$. 3. **Find the center of the circle:** The center $(h, k)$ of the circle is given by $$h = -\frac{D}{2}, \quad k = -\frac{E}{2}$$. Calculate: $$h = -\frac{1}{2} = -0.5$$ $$k = -\frac{0}{2} = 0$$ So, the center is at $$(-0.5, 0)$$. 4. **Use the midpoint formula for the diameter:** The center of the circle is the midpoint of the diameter. If one end is $(x_1, y_1) = (2, -3)$ and the other end is $(x_2, y_2)$, then the midpoint is: $$\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) = (h, k)$$ 5. **Set up equations for the other end:** $$\frac{2 + x_2}{2} = -0.5 \implies 2 + x_2 = -1 \implies x_2 = -3$$ $$\frac{-3 + y_2}{2} = 0 \implies -3 + y_2 = 0 \implies y_2 = 3$$ 6. **Final answer:** The coordinates of the other end of the diameter are $$\boxed{(-3, 3)}$$.