Question 130302
Your question is how many solutions, not how many real number solutions, or how many rational solutions.  That makes the question very easy to answer.  Just look at the highest exponent and that tells you how many solutions there are.  For your problem, the highest exponent is 2, so there are exactly 2 roots. They aren't necessarily real number solutions, they could be complex numbers involving the imaginary number i which is defined by {{{i^2=-1}}}, but there are always the same number of solutions as the degree (highest exponent) of the equation.