To find the real number solutions for the equation, we need to use the quadratic formula:
[tex] x = \frac{ - b( + - ) \sqrt{ {b}^{2} - 4ac } }{2a} [/tex]
(pardon the (+-), it is supposed to be a plus/minus sign) from the equation
[tex]a {x}^{2} + bx + c[/tex]
In this case, we have a = 1, b = -3, c = 8.
[tex] - ( - 3)[/tex]
[tex] \frac{ - ( - 3)( + - ) \sqrt{ {( - 3)}^{2} - 4(1)(8) } }{4(1)} \\ \frac{3( + - ) \sqrt{9 - 36} }{4} [/tex]
Since 9 - 36 is a negative number and we cannot square root a negative number, the answer is D. Cannot be determined.
