Can You Solve 2x^2-9x+10=0 Using The Quadratic Formula?

Yes. You can, too.
For quadratic
  a*x^2 + b*x + c = 0
The solution is
  x = (-b ±√(b^2 - 4*a*c))/(2*a)    (this is the quadratic formula)
You have a=2, b=-9, c=10. Making the substitutions, we get
  x = (-(-9) ±√((-9)^2 - 4*2*10))/(2*2)
  = (9 ±√(81-80))/4
  = (9±1)/4
  = {10/4, 8/4}
x = 2 1/2 or 2