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https://youtu.be/JwODg9lu-WI

(400d² - 480000)/(d² + 300) < 0 → you know that a square is always ≥ 0 → (d² + 300) > 0

400d² - 480000 < 0

400.(d² - 1200) < 0 → you know that: 400 > 0

d² - 1200 < 0

d² < 1200

- √1200 < d < √1200 → recall: 1200 = 400 * 3 = 20² * 3

- 20√3 < d < 20√3

-20 Sqrt[3]<d<20 Sqrt[3]

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(400 d^2-480000)/(d^2+300) < 0 ->

(400 d^2-480000) < 0 (d^2+300) ->

(400 d^2-480000) < 0 ->

400 d^2-480000 < 0 ->

400 d ^2 < 480000 ->

d^2 < 480000/400 ->

d^2 < 1200 ->

- Sqrt[1200] < d < Sqrt[1200] ->

- Sqrt[400 * 3] < d < Sqrt[400 * 3] ->

- 20 Sqrt[3] < d < 20 Sqrt[3]