$\frac{30}{x} - \frac{30}{x + 3} = \frac{1}{2}$
x ≠ 0
и
x + 3 ≠ 0
x ≠ −3
$\frac{30}{x} - \frac{30}{x + 3} = \frac{1}{2}$ | * 2x(x + 3)
30 * 2(x + 3) − 2x * 30 = x(x + 3)
$60x + 180 - 60x = x^2 + 3x$
$-x^2 - 3x + 180 = 0$ | * (−1)
$x^2 + 3x - 180 = 0$
$D = b^2 - 4ac = 3^2 - 4 * 1 * (-180) = 9 + 720 = 729 > 0$
$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{-3 + \sqrt{729}}{2 * 1} = \frac{-3 + 27}{2} = \frac{24}{2} = 12$
$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{-3 - \sqrt{729}}{2 * 1} = \frac{-3 - 27}{2} = \frac{-30}{2} = -15$
Ответ: при x = −15 и x = 12

$\frac{20}{x} - \frac{20}{x + 18} = 9$
x ≠ 0
и
x + 18 ≠ 0
x ≠ −18
$\frac{20}{x} - \frac{20}{x + 18} = 9$ | * x(x + 18)
20(x + 18) − 20x = 9x(x + 18)
$20x + 360 - 20x = 9x^2 + 162x$
$-9x^2 -162x + 360 = 0$ | : (−9)
$x^2 + 18x - 40 = 0$
$D = b^2 - 4ac = 18^2 - 4 * 1 * (-40) = 324 + 160 = 484 > 0$
$x_1 = \frac{-b + \sqrt{D}}{2a} = \frac{-18 + \sqrt{484}}{2 * 1} = \frac{-18 + 22}{2} = \frac{4}{2} = 2$
$x_2 = \frac{-b - \sqrt{D}}{2a} = \frac{-18 - \sqrt{484}}{2 * 1} = \frac{-18 - 22}{2} = \frac{-40}{2} = -20$
Ответ: при x = −20 и x = 2