Solve :

$\Big(\dfrac{1200}{x} + 2\Big)(x - 10) - 1200 = 60.$

Given,

$\Rightarrow \Big(\dfrac{1200}{x} + 2\Big)(x - 10) - 1200 = 60 \\[1em] \Rightarrow \dfrac{(1200 + 2x)(x - 10)}{x} = 60 + 1200 \\[1em] \Rightarrow \dfrac{1200x - 12000 + 2x^2 - 20x }{x} = 1260 \\[1em] \Rightarrow 2x^2 + 1180x - 12000 = 1260x \\[1em] \Rightarrow 2x^2 + 1180x -1260x - 12000 = 0 \\[1em] \Rightarrow 2x^2 - 80x - 12000 = 0 \\[1em] \Rightarrow 2(x^2 - 40x - 6000) = 0 \\[1em] \Rightarrow x^2 - 40x - 6000 = 0 \\[1em] \Rightarrow x^2 - 100x + 60x - 6000 = 0 \\[1em] \Rightarrow x(x - 100) + 60(x - 100) = 0 \\[1em] \Rightarrow (x + 60)(x - 100) = 0 \\[1em] \Rightarrow (x + 60) = 0 \text{ or } (x - 100) = 0 \\[1em] \Rightarrow x = -60 \text{ or } x = 100.$

Hence, x = -60 or 100.