Maximum altitude of a rocket

Ahmed.Sandman

Homework Statement

A rocket of mass 1.5 x 10^6 kg is launched upward from the surface of the Earth (mass ME = 5.97 x 10^24 kg, radius RE = 6.38 x 10^6 m) with a speed of 0.5 x 10^4 m/s. The rocket will reach a maximum altitude above the surface of the Earth of

Homework Equations

I thought I can solve it with the basic kinematic equations
v^2=v0^2+2*a*delta(x)

The Attempt at a Solution

the right answer is 6.061*10^6m (according to the online quiz)
but I can't reach that conclusion using the equation

I'm not using the Earth's radius or mass

You cannot assume a constant acceleration here. Equate the kinetic energy of the rocket at the surface of the Earth with it's potential energy at a height $h$ above its surface.