Find the number of real number solutions for the equation x^2-3+8=0

Find value of determinant.
The determinant is a term that is inside a square root and part of the quadratic formula used for solving quadratic equations.
Let determinant be 'd'.
If d >0, Then there are 2 real solutions
If d = 0, Then there is only 1 real solutions
If d < 0, Then there are 0 real solutions but 2 imaginary solutions

d = b^2 - 4ac

For this problem, the coefficients are:
a = 1, b = -3, c = 8

d = (-3)^2 - 4(1)(8)

d = 9 -32 = -23

d is less than 0, therefore there are 0 real solutions and 2 imaginary solutions.

This is true because you cannot take square root of a negative number.