At what redshift did the Universe beging accelerating?

[soothsayer]

Homework Statement

Starting with the equation for a'', derive an expression for the redshift at which the deceleration of the Universe turned into acceleration. Your expression should contain only fundamental cosmological parameters at the present day such as $$\Omega$$_M0 and $$\Omega$$_$$\Lambda$$0.

Homework Equations

Freidmann Acceleration equation:

Redshift-Scale Factor:

1+z=1/a

The Attempt at a Solution

I've literally been racking my brain for hours, trying to come up with every possible manipulation of this equation. I know a''=0 at the point where the universe stops decelerating and begins to accelerate, but the acceleration equation does seem to make any sense at this point, I tried expressing the Freidmann Equation in terms of $$\Omega$$_M0 and $$\Omega$$_$$\Lambda$$0, namely,

But I wasn't able to figure out any satisfactory way to manipulate this one.

 

[member 553083]

The other thing I tried was to express a'' in terms of 1+z and the scale factor, namely,Which is really close to what I need, but I still can't figure out how to get rid of the a^2 term. Any help would be appreciated.