The equations $x^2-7x+12=0$ and $x^2-9x+20=0$ have exactly one root in common. That root is:

Subtracting the second equation from the first eliminates $x^2$ and leaves $2x-8=0$, so any common root must be $x=4$ — and 4 does satisfy both. (Their root pairs are 3, 4 and 4, 5, so 3 and 5 are the roots that are not shared.)