\(\dfrac{350}{x}=\dfrac{360}{x+5}+1(x\ne -5)\\→350(x+5)=360x+x(x+5)\\↔350x+1750=360x+x^2+5x\\↔350x+1750=365x+x^2\\↔-x^2-15x+1750=0\\↔x^2+15x-1750=0\\↔x^2+2.7,5.x+56,25-1806,25=0\\↔(x+7,5)^2-1806,25=0\\↔(x+7,5-42,5)(x+7,5+42,5)=0\\↔(x-35)(x+50)=0\\↔\left[\begin{array}{1}x+50=0\\x-35=0\end{array}\right.\\↔\left[\begin{array}{1}x=-50(TM)\\x=35(TM)\end{array}\right.\\Vậy\,\,S=\{-50;35\}\)
