8b=1/b^2

Solution for 8b=1/b^2 equation:

D( b )

b^2 = 0

b^2 = 0

b^2 = 0

1*b^2 = 0 // : 1

b^2 = 0

b = 0

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

8*b = 1/(b^2) // - 1/(b^2)

8*b-(1/(b^2)) = 0

8*b-b^-2 = 0

8*b^1-1*b^-2 = 0

(8*b^3-1*b^0)/(b^2) = 0 // * b^4

b^2*(8*b^3-1*b^0) = 0

b^2

8*b^3-1 = 0

{ 1, -1 }

1

b = 1

8*b^3-1 = 7

1

-1

b = -1

8*b^3-1 = -9

-1

{ 1/2, -1/2, 1/4, -1/4, 1/8, -1/8, -1/2, 1/2, -1/4, 1/4, -1/8, 1/8 }

1/2

b

1/2

8*b^3-1 = 0

1/2

b-1/2

8*b^2+4*b+2

8*b^3-1

b-1/2

4*b^2-8*b^3

4*b^2-1

2*b-4*b^2

2*b-1

1-2*b

0

8*b^2+4*b+2 = 0

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

DELTA = -48

DELTA < 0

b in { 1/2} 

b = 1/2