You can put this solution on YOUR website! Strictly speaking, the equation will always have 2 solutions over the complex numbers. However, some of these solutions may be the same as each other (higher multiplicity). For example, x^2=0 has two solutions, they are both 0.
If you are are only looking for solutions over the real numbers then your statement is correct. It follows from observing that there is no number that when squared gives a negative result and that there is only one number that when squared gives 0, (0 itself). Of course you also know that all positive real numbers have two real roots (positive and negative).
(