Remember that solutions to quadratic equations indicate their x-intercepts, or where they cross the x axis. This one doesn't.
(Substituting 0 for y is the quickest/easiest way to find an x intercept on a problem like this.)
So 0 = x^2 + 4
Subtract 4 from both sides
-4 = x^2
Take the square root of both sides and you're left with...
x = sqrt -4, which is an imaginary number... perhaps useful in other maths but not for this equation.
No solutions, which in this case simply reinforces that the graph of this equation does not cross the x axis.