Actually it can... for example

if we expand it we get

has solutions x=2i and x=-3.

The question I think you are asking is...

Why cant a quadratic with REAL coefficients have both real and complex solutions.

Every quadratic can be solved using the quadratic fomula...

The discriminant tell us what type and how many solutions we will get.

To remind you it is the part under the radical

If it is positive you will get two different real solution.

If it is zero you get one repeated real solution.

if it is negative two complex solutions.

I hope this helps...