3n/3+(n+1/(3(5n+3)))

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Solution for 3n/3+(n+1/(3(5n+3))) equation:


D( n )

3*(5*n+3) = 0

3*(5*n+3) = 0

3*(5*n+3) = 0

5*n+3 = 0 // - 3

5*n = -3 // : 5

n = -3/5

n in (-oo:-3/5) U (-3/5:+oo)

1/(3*(5*n+3))+(3*n)/3+n = 0

1/(3*(5*n+3))+n+n = 0

1/(3*(5*n+3))+(3*n*(5*n+3))/(3*(5*n+3))+(3*n*(5*n+3))/(3*(5*n+3)) = 0

3*n*(5*n+3)+3*n*(5*n+3)+1 = 0

15*n^2+15*n^2+9*n+9*n+1 = 0

30*n^2+18*n+1 = 0

30*n^2+18*n+1 = 0

30*n^2+18*n+1 = 0

DELTA = 18^2-(1*4*30)

DELTA = 204

DELTA > 0

n = (204^(1/2)-18)/(2*30) or n = (-204^(1/2)-18)/(2*30)

n = (2*51^(1/2)-18)/60 or n = (-2*51^(1/2)-18)/60

(n-((-2*51^(1/2)-18)/60))*(n-((2*51^(1/2)-18)/60)) = 0

((n-((-2*51^(1/2)-18)/60))*(n-((2*51^(1/2)-18)/60)))/(3*(5*n+3)) = 0

((n-((-2*51^(1/2)-18)/60))*(n-((2*51^(1/2)-18)/60)))/(3*(5*n+3)) = 0 // * 3*(5*n+3)

(n-((-2*51^(1/2)-18)/60))*(n-((2*51^(1/2)-18)/60)) = 0

( n-((-2*51^(1/2)-18)/60) )

n-((-2*51^(1/2)-18)/60) = 0 // + (-2*51^(1/2)-18)/60

n = (-2*51^(1/2)-18)/60

( n-((2*51^(1/2)-18)/60) )

n-((2*51^(1/2)-18)/60) = 0 // + (2*51^(1/2)-18)/60

n = (2*51^(1/2)-18)/60

n in { (-2*51^(1/2)-18)/60, (2*51^(1/2)-18)/60 }

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