-\frac{1}{4} x^2 +2x + 1 > 0
a=-1/4, b=2, c=1, a<0 ramiona paraboli skierowane w dół
\Delta=b^2-4ac=2^2-4*(-\frac{1}{4})*1=4+1=5
\sqrt\Delta=\sqrt5
x_1=\frac{-b-\sqrt\Delta}{2a}=\frac{-2-\sqrt5}{2*(-\frac{1}{4})}=\frac{-2-\sqrt5}{-\frac{1}{2}}=(-2-\sqrt5)*(-2)=4+2\sqrt5=2(2+\sqrt5)\approx
\approx2(2+2,24)\approx2*4,24\approx8,48
x_2=\frac{-b+\sqrt2}{2}=\frac{-2+\sqrt5}{2*(-\frac{1}{4})}=\frac{-2+\sqrt5}{-\frac{1}{2}}=(-2+\sqrt5)*(-2)=4-2\sqrt5=2(2-\sqrt5)\approx
\approx2(2-2,24)\approx2*(-0,24)\approx-0,48
x\in ((2(2+\sqrt5);2(2-\sqrt5))
http://www.wolframalpha.com/input/?i=-%5Cfrac%7B1%7D%7B4%7D+x%5E2+%2B2x+%2B+1+%3E+0