Question

$5x-\frac{35}{x}=18,x\ne 0$

Answer 1

$$\begin{gathered} \text{Given:} \\ \text{5}x-\frac{35}{x}=18 \\ \Rightarrow 5x^2-35=18x\text{[Multiplying both side by}x] \\ \Rightarrow 5x^2-18x-35=0 \\ \Rightarrow 5x^2-(25x-7x)-35=0 \\ \Rightarrow 5x^2-25x+7x-35=0 \\ \Rightarrow 5x(x-5)+7(x-5)=0 \\ \Rightarrow (5x+7)(x-5)=0 \\ \Rightarrow 5x+7=0\text{or}x-5=0 \\ \Rightarrow x=\frac{-7}{5}\text{or}x=5 \\ \mathrm{H}\text{ence, the roots of the equation are}\frac{-7}{5}\text{and}5. \end{gathered}$$