a)
x^2-2x >3
x^2-2x-3>0
a=1, b=-2, c=-3
\Delta=b^2-4ac=4-4*1*(-3)=4+12=16
\sqrt\Delta=4
x_1=\frac{-b-\sqrt\Delta}{2a}=\frac{2-4}{2}=\frac{-2}{2}=-1
x_2=\frac{-b+\sqrt\Delta}{2a}=\frac{2+4}{2}=3
x\in(-\infty;-1)\cup(3;+\infty)
b)
(x+6)(x-2) <0
x_1=-6 , x_2=2 miejsca zerowe
x\in (-6;2)
c)
-y^2+8y <15
-y^2+8y-15<15
a=-1, b=8, c=-15
\Delta=64-4*(-1)*(-15)=64-60=4
\sqrt\Delta=2
x_1=\frac{-8-2}{2*(-1)}=\frac{-10}{-2}=5
x_2=\frac{-8+2}{-2}=\frac{-6}{-2}=3
a<0 ramiona paraboli skierowane w dół
http://www.wolframalpha.com/input/?i=-y%5E2%2B8y+%3C15
x\in (-\infty;3)\cup(5:+\infty)
d)
12y^2-11y+2 <0
a=12, b=-11, c=2
\Delta=121-4*12*2=121-96=25
\sqrt\Delta=5
x_1=\frac{11-5}{2*12}=\frac{6}{24}=\frac{1}{4}
x_2=\frac{11+5}{24}=\frac{16}{24}=\frac{2}{3}
x\in (\frac{1}{4};\frac{2}{3})
http://www.wolframalpha.com/input/?i=12y%5E2-11y%2B2+%3C0