cosmology - How long was the universe radiation dominated?

Using the Friedmann metric I've been trying to calculate how long the universe was radiation energy dominated. I've reduced the metric to:

$c.dt$ = $a(t).dr$

where a is the scale factor. I can work out the this since I know the redshift then was ~3000. But how do get rid of the dr and get an equation that relates $dt$ to $a(t)$ ?