I'd translate that as "Es gibt mehrere Lösungen". "Viele" really means "many".
E.g. in a mathematic equation, I'd understand "several" to mean two or four solutions, and "viele" would be for something like a² + b² = c² (okay, that one even has an infinite number of solutions), or for the question of "Which things can I use to fish my cat's toy from under the sofa?".