To determine the number and type of solutions, we use the general formula:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}.[/tex]In the given equation:
[tex]\begin{gathered} a=5, \\ b=-5, \\ c=6. \end{gathered}[/tex]Therefore:
[tex]x=\frac{5\pm\sqrt{25-120}}{10}.[/tex]From the determinant, we notice that the equation has complex solutions because it is negative.
Answer: Two complex solutions.
