Given a market demand function:
$$p=4-q-q^2$$
and the market supply function:
$$p=1+4q+q^2$$
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:
$$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$
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?
When you move arguments from right to left you get:
$3 - 5q - 2q^2 = 0$
and you can multiply this expression by (-1) and keep the equivalency, so you get:
$2q^2 + 5q - 3 = 0$
When you solve these for x, you will get the same solutions.
Edit: the solutions for x of both equations are 1/2 and -3, you must have missed something while putting the numbers in the formula. (put both these numbers instead of x, you should get an equality.) I can only assume you missed a minus somewhere, because the +/- operator sometimes confuses people.