Question

Solve: $\left(\frac{1200}{x}+2\right)(x-10)-1200=60$

Answer 1

Given:

$$\begin{gathered} \left(\frac{1200}{x}+2\right)(x–10)–1200=60 \\ \left(\frac{1200}{x}+2\right)(x–10)=1200+60 \\ \left(\frac{1200}{x}+2\right)(x–10)=1260 \\ (1200+2x)(x–10)=1260x \\ 1200x+2x^2–12000–20x=1260x \\ 2x^2+1200x–12000-20x-1260x=0 \\ 2x^2-80x–12000=0 \\ {x}^2–40x–6000=0 \\ {x}^2–100x+60x–6000=0 \\ x(x–100)+60(x–100)=0 \\ (x–100)(x+60)=0 \\ x=100orx=-60 \end{gathered}$$ $$\begin{gathered} \left[6000 \\ /\backslash \\ -100+60\right] \end{gathered}$$

Hence, $x=100orx=-60$.