Math problem help

Question

Twice a number plus 6 divided by four times the number is 8

Answer 1

This can be translated two ways:

(2n + 6) / 4n = 8

2n + 6 = 32n

6 = 30n

n =6/30 = 1/5

check;

2(1/5) + 6 divided by 4/5 =

(2/5+6) divided by 4/5 =

32/5 divided by 4/5

32/5 * 5/4 = 8

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2n + 6/(4n) = 8

2n + 3/(2n) = 8

4n^2 + 3 = 16n <--- multiplies both siddes by 2n

4n^2 - 16n + 3 = 0

n = [ 16 +or- sqrt( 256 - 4*4*3)]/8

= [ 16 +or- sqrt( 256 - 48)]/8

= [ 16 +or- sqrt(208)]/8

= [ 16 +or- sqrt(2*2*2*2*13))]/8

= [ 16 +or- 4*sqrt(13)]/8

= [ 4 +or- sqrt(13)]/2

I believe it is the first one