We know that one solution of the given elliptic curve is (2, 1) and we have to find another rational solution such that $x$ is not equal to 2 by drawing a tangent to the curve at (2, 1).
$$y^2=x^3- 7$$
However, by drawing a tangent at (2, 1), the line does not intersect the curve at any other point. How do I get another solution?
Do you know the group law (of an elliptic curve)? Assuming we're on a field of characteristic $\;\neq 2,3\;$ ,we can define:
$$t:=\frac{3\cdot 2^2}{2\cdot 1}=6$$
$$x_1:=t^2-2\cdot2=32\\y_1:=1+6(32-2)=181$$
and we get a new solution $\;(32\,,\,\,181)\;$