5/2n=8/(3n-24)

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Solution for 5/2n=8/(3n-24) equation:


D( n )

3*n-24 = 0

3*n-24 = 0

3*n-24 = 0

3*n-24 = 0 // + 24

3*n = 24 // : 3

n = 24/3

n = 8

n in (-oo:8) U (8:+oo)

(5/2)*n = 8/(3*n-24) // - 8/(3*n-24)

(5/2)*n-(8/(3*n-24)) = 0

(5/2)*n-8*(3*n-24)^-1 = 0

(5*n)/2-8/(3*n-24) = 0

(-8*2)/(2*(3*n-24))+(5*n*(3*n-24))/(2*(3*n-24)) = 0

5*n*(3*n-24)-8*2 = 0

15*n^2-120*n-16 = 0

15*n^2-120*n-16 = 0

15*n^2-120*n-16 = 0

DELTA = (-120)^2-(-16*4*15)

DELTA = 15360

DELTA > 0

n = (15360^(1/2)+120)/(2*15) or n = (120-15360^(1/2))/(2*15)

n = (32*15^(1/2)+120)/30 or n = (120-32*15^(1/2))/30

(n-((120-32*15^(1/2))/30))*(n-((32*15^(1/2)+120)/30)) = 0

((n-((120-32*15^(1/2))/30))*(n-((32*15^(1/2)+120)/30)))/(2*(3*n-24)) = 0

((n-((120-32*15^(1/2))/30))*(n-((32*15^(1/2)+120)/30)))/(2*(3*n-24)) = 0 // * 2*(3*n-24)

(n-((120-32*15^(1/2))/30))*(n-((32*15^(1/2)+120)/30)) = 0

( n-((120-32*15^(1/2))/30) )

n-((120-32*15^(1/2))/30) = 0 // + (120-32*15^(1/2))/30

n = (120-32*15^(1/2))/30

( n-((32*15^(1/2)+120)/30) )

n-((32*15^(1/2)+120)/30) = 0 // + (32*15^(1/2)+120)/30

n = (32*15^(1/2)+120)/30

n in { (120-32*15^(1/2))/30, (32*15^(1/2)+120)/30 }

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