Completing the square is represented by:
[tex]x^2+bx+(\frac{b}{2})^2+c=d+(\frac{b}{2})^2[/tex]Then,
[tex]\begin{gathered} x^2-6x+(\frac{-6}{2})^2=d+(-\frac{6}{2})^2 \\ x^2-6x+9+15=0+9 \\ x^2-6x+24=9 \\ \end{gathered}[/tex]By the rule of discriminant, we know that this expression has not real solutions.
[tex]\text{Discriminant}=(b^2-4ac)[/tex]If the discriminant is negative, the quadratic equation doesn't have real solutions.
