$2 \sqrt{x}-14=\frac{288}{\sqrt{x}}$

Step 1 ：Given the equation \(2 \sqrt{x}-14=\frac{288}{\sqrt{x}}\)

Step 2 ：Isolate the terms involving \(\sqrt{x}\) on one side of the equation and the constant term on the other side.

Step 3 ：Square both sides of the equation to get rid of the square root. This will give us a quadratic equation in \(\sqrt{x}\).

Step 4 ：Solve the quadratic equation using the quadratic formula.

Step 5 ：The solution to the equation is x = 256. This means that the value of x that satisfies the equation \(2 \sqrt{x}-14=\frac{288}{\sqrt{x}}\) is 256.

Step 6 ：Final Answer: \(\boxed{256}\)