# Avellaneda & Stoikov MM paper

I'm reading Avellaneda & Stoikov (2006) model for market making. On section 3.1, one can read

we are able to simplify the problem with the ansatz

$$u(s,x,q,t)=-\exp(-\gamma x)\exp (-\gamma\theta(s,q,t))$$

Direct substitution yields the following equation for $$\theta$$:

How the reservation prices $$r^b$$ and $$r^a$$ have been introduced in the equation?
Thank you