7h-1/(7h+1)=5/8

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Solution for 7h-1/(7h+1)=5/8 equation:


D( h )

7*h+1 = 0

7*h+1 = 0

7*h+1 = 0

7*h+1 = 0 // - 1

7*h = -1 // : 7

h = -1/7

h in (-oo:-1/7) U (-1/7:+oo)

7*h-(1/(7*h+1)) = 5/8 // - 5/8

7*h-(1/(7*h+1))-(5/8) = 0

7*h-(7*h+1)^-1-5/8 = 0

7*h-1/(7*h+1)-5/8 = 0

(-1*8)/(8*(7*h+1))+(7*8*h*(7*h+1))/(8*(7*h+1))+(-5*(7*h+1))/(8*(7*h+1)) = 0

7*8*h*(7*h+1)-5*(7*h+1)-1*8 = 0

392*h^2+56*h-35*h-8-5 = 0

392*h^2+21*h-13 = 0

392*h^2+21*h-13 = 0

392*h^2+21*h-13 = 0

DELTA = 21^2-(-13*4*392)

DELTA = 20825

DELTA > 0

h = (20825^(1/2)-21)/(2*392) or h = (-20825^(1/2)-21)/(2*392)

h = (35*17^(1/2)-21)/784 or h = (-35*17^(1/2)-21)/784

(h-((-35*17^(1/2)-21)/784))*(h-((35*17^(1/2)-21)/784)) = 0

((h-((-35*17^(1/2)-21)/784))*(h-((35*17^(1/2)-21)/784)))/(8*(7*h+1)) = 0

((h-((-35*17^(1/2)-21)/784))*(h-((35*17^(1/2)-21)/784)))/(8*(7*h+1)) = 0 // * 8*(7*h+1)

(h-((-35*17^(1/2)-21)/784))*(h-((35*17^(1/2)-21)/784)) = 0

( h-((-35*17^(1/2)-21)/784) )

h-((-35*17^(1/2)-21)/784) = 0 // + (-35*17^(1/2)-21)/784

h = (-35*17^(1/2)-21)/784

( h-((35*17^(1/2)-21)/784) )

h-((35*17^(1/2)-21)/784) = 0 // + (35*17^(1/2)-21)/784

h = (35*17^(1/2)-21)/784

h in { (-35*17^(1/2)-21)/784, (35*17^(1/2)-21)/784 }

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