`a,x^2-2003x-2004=0`
`⇒x^2+x-2004x-2004=0`
`⇒x(x+1)-2004(x+1)=0`
`⇒(x-2004)(x+1)=0`
\(⇒\left[ \begin{array}{l}x-2004=0⇒x=2004\\x+1=0⇒x=-1\end{array} \right.\)
`b, 2005x^2-2004x-1=0`
`⇒2005x^2-2005x+x-1=0`
`⇒2005x(x-1)+(x-1)=0`
`⇒(2015x+1)(x-1)=0`
\(⇒\left[ \begin{array}{l}2005x+1=0⇒2005x=-1⇒x=\dfrac{-1}{2005}\\x-1=0⇒x=1\end{array} \right.\)