The first part is to set the equations to 0 by moving everything to one side:
-4 = x2 - 5
Here we add 4 to both sides, giving us:
0 = x2 - 1
What we have here is a difference of two squares: the square root of x2 is x, and the square root of 1 is 1. This means that we can easily factor the problem out with one factor as positive and the other negative:
0 = (x + 1)(x - 1)
0 = x + 1, or 0 = x - 1
x = -1 or 1
When you check your answer putting these values into the original equation, you will see that 1 and -1 both will lead to a final answer of -4.
-4 = x2 + 2x
Again, we start by making the equation equal to 0 by moving everything to one side:
0 = x2 + 2x + 4
This equation has no real number solutions. We can take a look at its graph, and we can see the lowest point is going to be at the vertex of (-1, 3). It doesn't cross the x-intercept, so there are no solutions.