Can you help me prove that this ring is a field?

R = Q[$\displaystyle \sqrt(d)$] = { a+b$\displaystyle \sqrt(d)$ ; a,b are rational}

So I tried:

We must show that every element of R is a unit. So for some element (a+b*$\displaystyle \sqrt(d)$) there must be some (e+c*$\displaystyle \sqrt(d)$) such that

(a+b*$\displaystyle \sqrt(d)$)*(e+c*$\displaystyle \sqrt(d)$) = 1

so (ae+bed) + (be + ac)*$\displaystyle \sqrt(d)$ = 1

so ae-bed = 1 and be+ac =0

but then I get stuck after that