$\forall q$ determine the range of p to have distinct real roots for the following equation; $$x^2+(p-q)x+(1-p-q)=0$$
My Try
$\Delta\geq0$
$(p-q)^2-4(1-p-q)\geq0$
I know I have to isolate p in this inequality to get a range for p in terms of q.
$p^2+p(4-2q)+q^2+4q-4\geq0$
How should I proceed? Please help! Thanks