[latex]x^2-4x extgreater 0\ x(x-4) extgreater 0\ x=0 vee x-4=0\ x=0 vee x=4\ \ xin (-infty,0)cup(4,+infty)[/latex] [latex]-3(x-2)(x+5)ge 0\ -3x^2-9x+30ge 0\ Delta=(-9)^2-4cdot (-3)cdot 30=81+360=441\ sqrt{Delta}=sqrt{441}=21\ x_{1}=frac{9-21}{-6}=2\ x_{2}=frac{9+21}{-6}=-5\ \ xin extless -5,2 extgreater [/latex] [latex]3x^2+4x-4 extless 0\ Delta=4^2-4cdot 3cdot (-4)=16 + 48=64\ sqrt{64}=8\ x_{1}=frac{-4-8}{6}=-2\ x_{2}=frac{-4+8}{6}=frac{2}{3}\ \ xin (-2,frac{2}{3})[/latex] [latex]-2x^2+8le0 setminus :(-2)\ x^2-4ge0\ (x+2)(x-2)=0\ x=-2 vee x=2\ \ xin (-infty, -2 extgreater cup extless 2,+infty) [/latex]
x(do 2)-4x>0
xkwadrat-4x>0
-3(x-2)(x+5)>lub równe 0
-3(xkwadrat+5x-2x-10)>lub równe 0
-3xkwadrat-15x+6x+30>równe 0
-3xkwadrat-9x>równe-30
3x(do 2)+4x-4<0
3xkwadrat+4x<4
-2x(do2)+8
