Algorithm is a clearly defined procedure for obtaining the solution to a general type of problem, often numerical. Algorithm is a step-by-step problem-solving procedure, especially an established, recursive computational procedure for solving a problem in a finite number of steps. An algorithm might repeat in steps but it. So the problem can be solved. It might take a number of years but it doesn't take an infinite number of steps or infinite years. There are number of ways to solve a problem it depends on whether how u use the algorithm and in what ways there are always short cuts and long cuts.
If the long cut is chosen it might take a huge number of years. If you choose to do it the small way it might take few tears or even less time to solve it. It is like making food. Food can be made in two ways.
If you choose to make the food using old machineries it might take a very long time to make the food. And if choose to make the food using old machines it might take a very less amount of time. Either way you choose to do it one way takes a long time and the other takes the short time but it doesn't take an infinite number of steps an what ever problem we are solving does get solved. So yes I think that the it doesn't matter that the algorithm takes hundreds years to solve it does get solved and doesn't take forever to solve it and therefore it is solvable.