What are the real numbers for x^2-3x+8=0

Has no real solution (only imaginary solutions)

Step-by-step explanation:

x²-3x+8=0

recall for a quadratic equation in the form

ax² + bx + c = 0

the if b² - 4ac is negative (i. e less than zero), then the equation has no real solutions.

in this case,

a=1, b = - 3 and c=8

b² - 4ac,

= (-3) ² - (4) (1) (8)

= 9 - 32

= - 23 (negative number hence no real solutions)