b^2=6b/(6b-16)

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Solution for b^2=6b/(6b-16) equation:


D( b )

6*b-16 = 0

6*b-16 = 0

6*b-16 = 0

6*b-16 = 0 // + 16

6*b = 16 // : 6

b = 16/6

b = 8/3

b in (-oo:8/3) U (8/3:+oo)

b^2 = (6*b)/(6*b-16) // - (6*b)/(6*b-16)

b^2-((6*b)/(6*b-16)) = 0

b^2-6*b*(6*b-16)^-1 = 0

(-6*b)/(6*b-16)+b^2 = 0

(-6*b)/(6*b-16)+(b^2*(6*b-16))/(6*b-16) = 0

b^2*(6*b-16)-6*b = 0

6*b^3-16*b^2-6*b = 0

6*b^3-16*b^2-6*b = 0

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

3*b^2-8*b-3 = 0

DELTA = (-8)^2-(-3*3*4)

DELTA = 100

DELTA > 0

b = (100^(1/2)+8)/(2*3) or b = (8-100^(1/2))/(2*3)

b = 3 or b = -1/3

2*b*(b+1/3)*(b-3) = 0

(2*b*(b+1/3)*(b-3))/(6*b-16) = 0

(2*b*(b+1/3)*(b-3))/(6*b-16) = 0 // * 6*b-16

2*b*(b+1/3)*(b-3) = 0

( 2*b )

2*b = 0 // : 2

b = 0

( b+1/3 )

b+1/3 = 0 // - 1/3

b = -1/3

( b-3 )

b-3 = 0 // + 3

b = 3

b in { 0, -1/3, 3 }

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