4x=7+(1/x-1)

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Solution for 4x=7+(1/x-1) equation: 


D( x )

x = 0

x = 0

x = 0

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

4*x = 1/x-1+7 // - 1/x-1+7

4*x-(1/x)-7+1 = 0

4*x-x^-1-7+1 = 0

4*x^1-1*x^-1-6*x^0 = 0

(4*x^2-6*x^1-1*x^0)/(x^1) = 0 // * x^2

x^1*(4*x^2-6*x^1-1*x^0) = 0

x^1

4*x^2-6*x-1 = 0

4*x^2-6*x-1 = 0

DELTA = (-6)^2-(-1*4*4)

DELTA = 52

DELTA > 0

x = (52^(1/2)+6)/(2*4) or x = (6-52^(1/2))/(2*4)

x = (2*13^(1/2)+6)/8 or x = (6-2*13^(1/2))/8

x in { (6-2*13^(1/2))/8, (2*13^(1/2)+6)/8} 

x in { (6-2*13^(1/2))/8, (2*13^(1/2)+6)/8 }

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