It is called an equation with no solutions in the domain under consideration. It is quite possible that an equation which does not have a solution in one domain has a simple solution in another - possibly broader - domain.
For example,
Also, there are equations which cannot be solved analytically, but do have solutions which can be found by numerical methods.
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a solution
It's called the "solution" of the equation.
The solution set is the answers that make an equation true. So I would call it the solution.
It's called a solution
A number that makes an equation true is a solution. If there is more than one answer to an equation (such as an equation like): (x-2)(x+4)=0 then it is called a solution set (and in this case would be x={-4, 2}).