[tex]f(x) > g(x)\\\\3x^{2}-x > x^{2}-2x+3\\\\3x^{2}-x^{2}-x+2x-3 > 0\\\\2x^{2}+x-3 > 0\\\\a = 2, \ b = 1, \ c = -3\\\\\Delta = b^{2}-4ac = 1^{2}-4\cdot2\cdot(-3) = 1+24 = 25\\\\\sqrt{\Delta} = \sqrt{25} = 5\\\\x_1 = \frac{-b-\sqrt{\Delta}}{2a} = \frac{-1-5}{2\cdot2}=\frac{-6}{4} = -1,5\\\\x_2 = \frac{-b+\sqrt{\Delta}}{2a} = \frac{-1+5}{2\cdot2} = \frac{4}{4} = 1[/tex]
a > 0, to ramiona paraboli skierowane do góry, wartości > 0 znajdują się nad osią OX
x ∈ (-∞; -1,5) ∪ (1; +∞)
