a) \(x^2-10=25\Leftrightarrow x^2=35\Leftrightarrow x=\pm\sqrt{35}\)
b) \(\left(x-1\right)\left(x+2\right)-x\left(x-2\right)=-5\)
\(\Leftrightarrow x^2+2x-x-2-x^2+2x=-5\)
\(\Leftrightarrow3x-2=-5\Leftrightarrow3x=-3\Leftrightarrow x=-1\)
c) \(7x^2+2x=0\Leftrightarrow x\left(7x+2\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\\7x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-\dfrac{2}{7}\end{matrix}\right.\)
d) \(x^2-25-\left(x+5\right)=0\)
\(\Leftrightarrow x^2-25-x-5=0\)
\(\Leftrightarrow x^2-x-30=0\)
\(\Leftrightarrow\left(x-6\right)\left(x+5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-6=0\\x+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=6\\x=-5\end{matrix}\right.\)