SOLUTION: Solve this quadratic inequality and show answer in interval notation: 4x^2 - 12x + 9 > 0

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Question 367588: Solve this quadratic inequality and show answer in interval notation:
4x^2 - 12x + 9 > 0
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
4x%5E2+-+12x+%2B+9+%3E+0+ is the same as %282x-3%29%5E2+%3E0. All real numbers will satisfy this except x = 3/2, when it is zero. Thus the solution set is (-infinity, 3/2)U(3/2, infinity).
4x^2 - 3x - 6 = 0
Check the discriminant:b%5E2-4%2Aa%2Ac+=+%28-3%29%5E2+-+4%2A4%2A-6+=+9+%2B96=105. The value of the discriminant is positive but is not a perfect square, so the quadratic expression cannot be factored into linear factors with rational coefficients.