Hi there!
We can use the discriminant of the quadratic formula to find the number of real solutions to this (or any other quadratic) equation.
The discriminant can be found by plugging in the data from the equation into the following formula:
[tex]d = {b}^{2} - 4ac \\ with \: y \: = a {x}^{2} + bx + c[/tex]
When we fill in the data from the question we get
[tex]d = ( - 2) {}^{2} - 4 \times 1 \times 9 = 4 - 36 = - 32[/tex]
Since d < 0 the equation has zero real solutions.
