nature of roots

Hi friends,

I have something that tickles me....please help:

if I look at \(x^2-4x-5=0\)

and I wanted to check the nature of the roots by solving the equation, it would be like this:

\((x+1)(x-5)=0\)

\(x=-1\)  or  \(x=5\)

So all I can really say is that the roots are un-equal

However doing it this way:

\(\Delta =b^2-4ac\)

    \(=(-4)^2-4(1)(-5)\)

    \(=16+20\)

    \(=36\)

which means the roots will be real, un-equal and rational...However, the roots do only seem to satisfy the "un-equal" nature?