Four problems:
Problem 1:
3x - 2 = 2sqrt(x) + 8
3x - 10 = 2sqrt(x)
9x^2 - 60x + 100 = 4x
9x^2 - 64x + 100 = 0
x = (64 +- sqrt(4096 - 3600))/18
x = (64 +- sqrt(496))/18
x = (64 +- 4sqrt(31))/18
x = (32 +- 2sqrt(31))/9
x = (32 + 2sqrt(31))/9, (32 - 2sqrt(31))/9
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Problem 2
-3x + 2 = 2sqrt(x) + 8
-3x - 6 = 2sqrt(x)
9x^2 + 36x + 36 = 4x
9x^2 + 32x + 36 = 0
x = (-32 +- sqrt(1024 - 1296))/18
Can't do square root of a negative, so no solution.
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Problem 3
3x - 2 = 2sqrt(x + 8)
9x^2 - 12x + 4 = 4(x+8)
9x^2 - 12x + 4 = 4x + 32
9x^2 - 16x - 28 = 0
x = (16 +- sqrt(256 + 36*28))/18
x = (16 +- sqrt(256 + 1008))/18
x = (16 +- sqrt(1264))/18
x = (16 +- 4sqrt(79))/18
x = (8 +- 2sqrt(79))/9
x = (8 + 2sqrt(79))/9, (8 - 2sqrt(79))/9
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Problem 4:
-3x + 2 = 2sqrt(x+8)
9x^2 - 12x + 4 = 4(x+8)
9x^2 - 12x + 4 = 4x + 32
9x^2 - 16x - 28 = 0
same as Problem 3
x = (8 + 2sqrt(79))/9, (8 - 2sqrt(79))/9
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Answer:
If you meant abs(3x-2) = 2sqrt(x) + 8 then the answer is: x = (32 + 2sqrt(31))/9, (32 - 2sqrt(31))/9
If you meant abs(3x-2) = 2sqrt(x+8) then the answer is: x = (8 + 2sqrt(79))/9, (8 - 2sqrt(79))/9