1. **State the problem:** Solve the equation $$\partial^2 \sqrt{5x} - 14 = 0$$. 2. **Interpret the problem:** The symbol $$\partial^2$$ usually denotes a second partial derivative, but here it seems to be used as a second derivative or a notation error. Assuming the problem is to solve $$\sqrt{5x} - 14 = 0$$ for $$x$$. 3. **Rewrite the equation:** $$\sqrt{5x} - 14 = 0$$ 4. **Isolate the square root term:** $$\sqrt{5x} = 14$$ 5. **Square both sides to eliminate the square root:** $$\left(\sqrt{5x}\right)^2 = 14^2$$ $$5x = 196$$ 6. **Solve for $$x$$:** $$x = \frac{196}{5}$$ 7. **Simplify the fraction:** $$x = 39.2$$ 8. **Check the solution:** Substitute back into the original equation: $$\sqrt{5 \times 39.2} - 14 = \sqrt{196} - 14 = 14 - 14 = 0$$ which is true. **Final answer:** $$x = 39.2$$