Solving Equation: 2√x - 14 = 288/√x

The equation given is:

Let’s start by multiplying both sides by to eliminate the fraction on the right side:

Now, let’s rearrange the equation to standard form:

This is a quadratic equation in terms of . Let’s substitute :

Now we can solve this using the quadratic formula:
Where , , and

Plugging into the quadratic formula:

Simplifying:

This gives us two solutions:

or

Remember that , so . Since we can’t have a negative square root, we only consider the positive solution: