Linear market equilibrium

Statement

Demand is $D(p)=180-3p$ and supply is $S(p)=2p-20$ (with $p$ in €). Find the equilibrium price and quantity.

Solution

At equilibrium $D(p)=S(p)$: $180-3p=2p-20\iff 200=5p\iff p^{*}=40\ \text{€}.$ Quantity: $q^{*}=2\cdot 40-20=60$ (check: $D(40)=180-120=60$ ✓). $\boxed{(p^{*};\,q^{*})=(40\ \text{€};\,60)}$