(n-1/(4n-6))-1/4

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Solution for (n-1/(4n-6))-1/4 equation:


D( n )

4*n-6 = 0

4*n-6 = 0

4*n-6 = 0

4*n-6 = 0 // + 6

4*n = 6 // : 4

n = 6/4

n = 3/2

n in (-oo:3/2) U (3/2:+oo)

n-(1/(4*n-6))-(1/4) = 0

n-(4*n-6)^-1-1/4 = 0

n-1/(4*n-6)-1/4 = 0

(-1*4)/(4*(4*n-6))+(4*n*(4*n-6))/(4*(4*n-6))+(-1*(4*n-6))/(4*(4*n-6)) = 0

4*n*(4*n-6)-1*(4*n-6)-1*4 = 0

16*n^2-24*n-4*n-4+6 = 0

16*n^2-28*n+2 = 0

16*n^2-28*n+2 = 0

2*(8*n^2-14*n+1) = 0

8*n^2-14*n+1 = 0

DELTA = (-14)^2-(1*4*8)

DELTA = 164

DELTA > 0

n = (164^(1/2)+14)/(2*8) or n = (14-164^(1/2))/(2*8)

n = (2*41^(1/2)+14)/16 or n = (14-2*41^(1/2))/16

2*(n-((14-2*41^(1/2))/16))*(n-((2*41^(1/2)+14)/16)) = 0

(2*(n-((14-2*41^(1/2))/16))*(n-((2*41^(1/2)+14)/16)))/(4*(4*n-6)) = 0

(2*(n-((14-2*41^(1/2))/16))*(n-((2*41^(1/2)+14)/16)))/(4*(4*n-6)) = 0 // * 4*(4*n-6)

2*(n-((14-2*41^(1/2))/16))*(n-((2*41^(1/2)+14)/16)) = 0

( 2 )

2 = 0

n belongs to the empty set

( n-((14-2*41^(1/2))/16) )

n-((14-2*41^(1/2))/16) = 0 // + (14-2*41^(1/2))/16

n = (14-2*41^(1/2))/16

( n-((2*41^(1/2)+14)/16) )

n-((2*41^(1/2)+14)/16) = 0 // + (2*41^(1/2)+14)/16

n = (2*41^(1/2)+14)/16

n in { (14-2*41^(1/2))/16, (2*41^(1/2)+14)/16 }

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