Energy Method: Inclined Plane - Solving for Velocity and Time

[e101101]

Homework Statement

Mechanics

Relevant Equations

E=1/2m(dx/dt)^2+mgh
Integrals

So far I've got
E=1/2m(dx/dt)^2+mgh
this can be rewritten as
(dx/dt)^2=2(E-mgxsin(Θ))/m

Would there not be a positive and negative solution?
dx/dt=±sqrt(2(E-mgxsin(Θ))/m) or do we discard the negative one? Why would we do so, if that's the case.
So far I've only solved the positive solution and have gotten:
t^2gsin(Θ)/2-tv=x(t)

 

[haruspex]

E=1/2m(dx/dt)^2+mgh

That equation is true whether the velocity is up or down the plane. Indeed, it will slide up the plane at first but then slide down, so at each value of x the velocity can have either sign. Which to use must be determined by other information. E.g., you know the sign at t=0.