\(\left(2x-5\right)\left(x-3\right)=2x^2+2004\)
\(2x^2-6x-5x+15=2x^2+2004\)
\(2x^2-11x+15=2x^2+2004\)
\(2x^2-2x^2-11x=2004-15\)
\(-11x=1989\)
\(x=1989:-11\)
\(x=-\frac{1989}{11}\)
\(\left(2x-5\right)\left(x-3\right)=2x^2+2004\)
\(\Rightarrow2x^2-6x-5x+15=2x^2+2004\)
\(\Rightarrow\left(2x^2-2x^2\right)-\left(6x+5x\right)=2004-15\)
\(\Rightarrow-11x=1989\)
\(\Rightarrow x=-\frac{1989}{11}\)