What types of solutions does this equation have?

Two imaginary solutions.

Step-by-step explanation:

In order to simplify the equation, we square root both sides. As the argument (value in the root) is negative, and we know that the square root function's domain is only positive numbers, we would have two imaginary solutions.

This would be positive/negative .

Another way to visualize this is by looking at the parabola's graph. Through algebraic manipulation, we know that the parabola is z^2 + 45. This parabola never crosses the x-axis. Therefore there are two solutions that are imaginary.

I hope this helps!