the solutions of an equation are the values of the variables for which the equation is true. but for algebraic equations there are also called roots. when solving an equation, we need to say in which set the solutions are allowed. for example, for an equation over the rationals, one can find solutions in the integers. then, the equation is a diophantine equation. one may also look for solutions in the field of complex numbers. one can also look for solutions in real numbers.