The equation ax^2+bx+c = 0 has a real solution if b^2-4ac>=0
We have to determine if x^2=-64 has real solutions.
=> x^2 + 64 = 0
b^2 - 4ac = -4*64 = -256 which is less than 0.
The equation x^2=-64 does not have a real solution.
Of course, not!
There is no real number that raised to square to give a negative value.
But the equation has complex solutions.
x1 = +sqrt(-64) =>x1 = 8i
x2 = -sqrt(-64) => x2 = -8i
Keep in mind that complex solutions always come in pairs!
Therefore, the given equation has no real solutions.