The given equation is x - 8\(\sqrt{x}\) + 15 = 0. Let y = \(\sqrt{x}\), then the equation becomes y^2 - 8y + 15 = 0. 

This is a quadratic equation, which can be solved by factoring or using the quadratic formula. Factoring, we get (y - 3)(y - 5) = 0. 

So, the solutions for y are y = 3 and y = 5. Since y = \(\sqrt{x}\), we have \(\sqrt{x}\) = 3 and \(\sqrt{x}\) = 5. 

Squaring both sides of these equations, we get x = 9 and x = 25.