\(\left(4x+1\right)\left(-4x+1\right)-16x\left(-5\right)=17\)
\(\Leftrightarrow\left(1+4x\right)\left(1-4x\right)+80x-17=0\)
\(\Leftrightarrow1-16x^2+80x-17=0\)
\(\Leftrightarrow-16x^2-16+80x=-16\left(x^2-5x+1\right)=0\Leftrightarrow-16\left[\left(x^2-5x+\dfrac{25}{4}\right)-\dfrac{21}{4}\right]=0\Leftrightarrow-16\left(x-\dfrac{5}{2}\right)^2+84=0\Rightarrow\left(x-\dfrac{5}{2}\right)^2=\dfrac{21}{4}\) \(\Rightarrow\left[{}\begin{matrix}x-\dfrac{5}{2}=\sqrt{\dfrac{21}{4}}\\x-\dfrac{5}{2}=-\sqrt{\dfrac{21}{4}}\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=\sqrt{\dfrac{21}{4}}+\dfrac{5}{2}\\x=-\sqrt{\dfrac{21}{4}}+\dfrac{5}{2}\end{matrix}\right.\)
