Question 41895
Comparing the given equation {{{2x^2-7x+9=0}}} with the standard quadratic equation {{{ax^2+bx+c=0}}} we find a = 2, b = -7, c = 9.


The discriminant is {{{D = b^2-4ac}}}.
Then if the coefficients i.e. a, b, c are real:
1) If D > 0, the roots are real but unequal.
2) If D = 0, the roots are real and equal.
3) If D < 0, the roots are imaginery and conjugate.


Special case: 
If D > 0, D is a perfect square and the coefficients are also rational then the roots are also rational.


Here, {{{D = (-7)^2 - 4*2*9}}} = 49 - 72 = -23.
Hence, D < 0, also the coefficients are real and so the roots are imaginery and conjugate.

For a brief discussion on rational numbers you may see my lesson at
http://www.algebra.com/tutors/INTRODUCTION_TO_RATIONAL_AND_IRRATIONAL_NUMBERS.lesson?content_action=show_dev