5/3n-1/9=1/n

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Solution for 5/3n-1/9=1/n equation:


D( n )

n = 0

n = 0

n = 0

n in (-oo:0) U (0:+oo)

(5/3)*n-(1/9) = 1/n // - 1/n

(5/3)*n-(1/n)-(1/9) = 0

(5/3)*n-n^-1-1/9 = 0

5/3*n^1-1*n^-1-1/9*n^0 = 0

(5/3*n^2-1/9*n^1-1*n^0)/(n^1) = 0 // * n^2

n^1*(5/3*n^2-1/9*n^1-1*n^0) = 0

n^1

(5/3)*n^2+(-1/9)*n-1 = 0

(5/3)*n^2+(-1/9)*n-1 = 0

DELTA = (-1/9)^2-(-1*4*(5/3))

DELTA = 541/81

DELTA > 0

n = ((541/81)^(1/2)-(-1/9))/(2*(5/3)) or n = (-(-1/9)-(541/81)^(1/2))/(2*(5/3))

n = 3/10*((541/81)^(1/2)+1/9) or n = 3/10*(1/9-(541/81)^(1/2))

n in { 3/10*(1/9-(541/81)^(1/2)), 3/10*((541/81)^(1/2)+1/9)}

n in { 3/10*(1/9-(541/81)^(1/2)), 3/10*((541/81)^(1/2)+1/9) }

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