Given a market demand function:
and the market supply function:
We can solve for:
$$4-q-q^2 = 1+4q+q^2$$
When I move the terms from right to left, I get $3-5q-2q^2$, but from left to right $2q^2+5q-3$.
I understand multiplying by $-1$ will give me the inverse of the other.
To determine the equilibrium price and quantity, we can use the quadratic formula:
However, this will give a different result depending on which direction I have collected the terms.
My question is therefore, how do I know which of the two I use to solve the problem?