Solve for y: y+4sqrt(y)=x

Question

Solve for y:

Answer 1

Let u = √y

Then the equation can be rewritten as u² + 4u - x = 0, which is a quadratic equation in the variable u.

Applying the quadratic formula, we get u = [-4 ± √{16+4x)] / 2 = [-4 ± 2√(4+x)] / 2 = -2 ± √(4+x)

Since u = √y, y = u² = (-2 ± √(4+x))².