a)
[tex]2x^{2}-4x > 3x^{2}-6x\\\\2x^{2}-3x^{2} > -6x+4x\\\\-x^{2}>-2x\\\\-x^{2}+2x>0 \ \ /:(-1)\\\\\underline{x^{2}-2x < 0}\\\\M. \ zerowe:\\\\x(x-2) = 0\\\\x = 0 \ \vee \ x-2\\\\x = 0 \ \vee \ x = 2\\\\a > 0, \ to \ ramiona \ wykesu \ paraboli \ skierowane \ do \ gory\\\\\boxed{x \in(0;4)}[/tex]
b)
[tex]2x^{2}-4x > (x+3)(x-2)\\\\2x^{2}-4x>x^{2}-2x+3x-6\\\\2x^{2}-4x>x^{2}+x-6\\\\2x^{2}-x^{2}-4x-x+6>0\\\\x^{2}-5x+6 > 0\\\\a = 1, \ b = -5, \ c = 6\\\\\Delta = b^{2}-4ac = (-5)^{2}-4\cdot1\cdot6 = 25-24 = 1\\\\\sqrt{\Delta} = \sqrt{1} = 1\\\\x_1 = \frac{-b-\sqrt{\Delta}}{2a} = \frac{5-1}{2} = \frac{4}{2} = 2\\\\x_2 = \frac{-b+\sqrt{\Delta}}{2a} = \frac{5+1}{2} = \frac{6}{2} =3\\\\a > 0, \ to \ ramiona \ wykresu \ paraboli \ skierowane \ do \ gory\\\\\boxed{x \in (-\infty; 2) \ \cup \ (3;+\infty)}[/tex]
c)
[tex]3x-x^{2}\geq 0 \ \ /\cdot(-1)\\\\\underline{x^{2}-3x \leq 0}\\\\M. \ zerowe:\\\\x^{2}-3x = 0\\\\x(x-3) = 0\\\\x = 0 \ \vee \ x = 3\\\\a > 0, \ to \ ramiona \ paraboli \ skierowane \ do \ gory\\\\\boxed{x \in \langle0;3\rangle}[/tex]
d)
[tex](2x-3)(3-x)\geq 0\\\\2x-3 = 0 \ \vee \ 3-x = 0\\\\2x = 3 \ \vee \ -x = -3\\\\x = 1,5 \ \vee \ x = 3\\\\a < 0, \ to \ ramiona \ paraboli \ skierowane \ do \ dolu\\\\\boxed{x \in \langle1,5; 3\rangle}[/tex]
