[tex]\lim_{x\rightarrow 4}\frac{6\sqrt{5+x}+2\sqrt{5-x}-20}{(x-4)^2}=\\=\lim_{x\rightarrow 4}\frac{6\sqrt{5+x}-18+2\sqrt{5-x}-2}{(x-4)^2}\\=\lim_{x\rightarrow 4}\frac{6\frac{x-4}{\sqrt{5+x}+3}-2\frac{x-4}{\sqrt{5-x}+1}}{(x-4)^2}\\=\lim_{x\rightarrow 4}\frac{\frac{6}{\sqrt{5+x}+3}-\frac{2}{\sqrt{5-x}+1}}{x-4}\\=\lim_{x\rightarrow 4}\frac{6(\frac{3\sqrt{5-x}-\sqrt{5+x}}{3(\sqrt{5+x}+3)(\sqrt{5-x}+1)})}{x-4}\\=\lim_{x\rightarrow 4}\frac{6\frac{40-10x}{3(\sqrt{5+x}+3)(\sqrt{5-x}+1)(3\sqrt{5-x}+\sqrt{5+x})}}{x-4}\\=\lim_{x \to 4}\frac{-60}{3(\sqrt{5+x}+3)(\sqrt{5-x}+1)(3\sqrt{5-x}+\sqrt{5+x})}\\=\frac{-5}{18}[/tex]