`sqrt(7x+2)-sqrt(5-x)=(8x-3)/5`

`\sqrt{7x + 2} - \sqrt{5 - x} = (8x - 3)/5` 

ĐKXĐ: `(-2)/7 <= x <= 5`

PT `<=> [(\sqrt{7x + 2} - \sqrt{5 - x}).(\sqrt{7x + 2}+ \sqrt{5 - x})]/(\sqrt{7x + 2}+ \sqrt{5 - x}) = (8x - 3)/5` 

`<=> [7x + 2 - (5 - x)]/(\sqrt{7x + 2}+ \sqrt{5 - x}) = (8x - 3)/5`

`<=> [7x + 2 - 5 + x]/(\sqrt{7x + 2}+ \sqrt{5 - x}) = (8x - 3)/5`

`<=> [8x - 3]/(\sqrt{7x + 2}+ \sqrt{5 - x}) = (8x - 3)/5`

`<=> [8x - 3]/(\sqrt{7x + 2}+ \sqrt{5 - x}) - (8x - 3)/5 = 0`

`<=> (8x - 3).(1/(\sqrt{7x + 2}+ \sqrt{5 - x}) - 1/5) = 0`

TH1: `8x - 3 = 0 -> x = 3/8` `(tm)`

TH2: `1/(\sqrt{7x + 2}+ \sqrt{5 - x}) - 1/5 = 0`

`-> 1/(\sqrt{7x + 2}+ \sqrt{5 - x}) = 1/5`

`-> \sqrt{7x + 2}+ \sqrt{5 - x} = 5`

`-> 6x + 7 + 2\sqrt{(7x + 2).(5 - x)} = 25`

`-> 2\sqrt{(7x + 2).(5 - x)} = 18 - 6x`

`-> \sqrt{(7x + 2).(5 - x)} = 9 - 3x` `(x <= 3)`

`-> (7x + 2).(5 - x) = 81 - 54x + 9x^2`

`-> -7x^2 + 33x + 10 = 81 - 54x + 9x^2`

`-> 16x^2 - 87x + 71 = 0`

`-> x = 1` `(tm)` hoặc `x = 71/16` `(ktm)`

Vậy `x in {3/8;  1}`