Answer
Discriminant = 97; 2 unequal real and irrational conjugate solutions
Work Step by Step
$2x^2-11x+3=0$
Plug the coefficients into the discriminant of the quadratic formula.
$a=2, b=-11, c=3$
$\sqrt {b^2-4ac}$
$\sqrt {(-11)^2-4(2)(3)}$
$\sqrt {121-24}$
$\sqrt {97}$
Since the discriminant is greater than $0$, the equation has two unequal real and irrational conjugate solutions.