Yes I used the search function.
Let us suppose we have two simple supply and demand equations
$$Q_d = 20 – 2P$$ $$Q_s = -10 + 2P$$ To find where $Q_S = Q_d$ we put the two equations together
$$20-2P = -10 + 2P$$ $$20+10= 4P$$ $$\frac{30}{4}=P$$ $$P = 7.5$$ To find $Q$, we just put this value of $P$ into one of the equations
$$Q = 20 – (2×7.5)$$ $$Q= 5$$
in the example above it defines $Q_s$ and $Q_d$ now to my understanding that would mean quantity of demand and supply still is there a rule to this? is putting a Capital next to a Lower Case just a way to define two words together? Like saying having a $Q$ + $q$ means two different quantities still would putting $Q_f$ and $Q_s$ suffice also as saying first quantity and second quantity?
In many instances, like this one here, you'll have a set of variables which are all very similar, and so instead of labelling them ${A,B,C,D...}$, we would instead use ${x_A, x_B, x_C, x_D...}$ or ${x_1,x_2, x_3, x_4...}$. In this case, $Q$ means quantity, so $Q_s$ simply means "Quantity of Supply", while $Q_d$ means "Quantity of Demand". Since they're both quantities, it makes better sense to link them together.