If the graph of the functions does not pass through the x axis it has no real solutions, only complex ones.
An example would be x^2 + 5x + 11
To find the solutions you could use the quadratic formula.
x = [-5 +/- sqrt( 5^2 - 4*1*11) ] / 2
x = [-[5 +/- sqrt (-19) ] / 2
solutions are -5/2 +1/2 (sqrt 19)i and -5/2 - 1/2(sqrt19)i