\(a,\left(x+2\right)\left(x-2\right)+4x=4+x^2\)
\(\Leftrightarrow x^2-4+4x-4-x^2=0\)
\(\Leftrightarrow4x=16\)
\(\Rightarrow x=4\)
\(b,2\left(x+5\right)\left(x-5\right)+5x=8+x^2\)
\(\Leftrightarrow2x^2-50+5x-8-x^2=0\)
\(\Leftrightarrow x^2-5x-42=0\Rightarrow\left(x^2-5x+\dfrac{25}{4}\right)-\dfrac{193}{4}=0\Rightarrow\left(x-\dfrac{5}{2}\right)^2=\dfrac{193}{4}\Rightarrow\left[{}\begin{matrix}x-\dfrac{5}{2}=\sqrt{\dfrac{193}{4}}\\x-\dfrac{5}{2}=-\sqrt{\dfrac{193}{4}}\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=\sqrt{\dfrac{193}{4}}+\dfrac{5}{2}\\x=-\sqrt{\dfrac{193}{4}}+\dfrac{5}{2}\end{matrix}\right.\)
\(c,\left(x+4\right)^2-\left(x+1\right)\left(x-1\right)=16\)
\(\Leftrightarrow x^2+8x+16-x^2-1-16=0\)
\(\Leftrightarrow8x-1=0\Leftrightarrow8x=1\Rightarrow x=\dfrac{1}{8}\)
\(d,\left(2x-1\right)^2+\left(x+3\right)^2-5\left(x+7\right)\left(x-7\right)=0\)\(\Leftrightarrow4x^2-4x+1+x^2+6x+9-5x^2-245=0\)\(\Leftrightarrow2x=235\Leftrightarrow x=117,5\)