(2*x+1)/x+4+x/(2*x+1)=8.02

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Solution for (2*x+1)/x+4+x/(2*x+1)=8.02 equation: 


D( x )

2*x+1 = 0

x = 0

2*x+1 = 0

2*x+1 = 0

2*x+1 = 0 // - 1

2*x = -1 // : 2

x = -1/2

x = 0

x = 0

x in (-oo:-1/2) U (-1/2:0) U (0:+oo)

(2*x+1)/x+x/(2*x+1)+4 = 8.02 // - 8.02

(2*x+1)/x+x/(2*x+1)-8.02+4 = 0

((2*x+1)^2)/(x*(2*x+1))+(x^2)/(x*(2*x+1))+(-8.02*x*(2*x+1))/(x*(2*x+1))+(4*x*(2*x+1))/(x*(2*x+1)) = 0

(2*x+1)^2-8.02*x*(2*x+1)+4*x*(2*x+1)+x^2 = 0

5*x^2-16.04*x^2+8*x^2+4*x-8.02*x+4*x+1 = 0

8*x^2-11.04*x^2-4.02*x+4*x+1 = 0

1-3.04*x^2-0.02*x = 0

1-3.04*x^2-0.02*x = 0

1-3.04*x^2-0.02*x = 0

DELTA = (-0.02)^2-(-3.04*1*4)

DELTA = 0.02^2+12.16

DELTA = 12.1604

DELTA > 0

x = ((0.02^2+12.16)^(1/2)+0.02)/(-3.04*2) or x = (0.02-(0.02^2+12.16)^(1/2))/(-3.04*2)

x = -0.16447368*((0.02^2+12.16)^(1/2)+0.02) or x = -0.16447368*(0.02-(0.02^2+12.16)^(1/2))

(x+0.16447368*((0.02^2+12.16)^(1/2)+0.02))*(x+0.16447368*(0.02-(0.02^2+12.16)^(1/2))) = 0

((x+0.16447368*((0.02^2+12.16)^(1/2)+0.02))*(x+0.16447368*(0.02-(0.02^2+12.16)^(1/2))))/(x*(2*x+1)) = 0

((x+0.16447368*((0.02^2+12.16)^(1/2)+0.02))*(x+0.16447368*(0.02-(0.02^2+12.16)^(1/2))))/(x*(2*x+1)) = 0 // * x*(2*x+1)

(x+0.16447368*((0.02^2+12.16)^(1/2)+0.02))*(x+0.16447368*(0.02-(0.02^2+12.16)^(1/2))) = 0

( x+0.16447368*((0.02^2+12.16)^(1/2)+0.02) )

x+0.16447368*((0.02^2+12.16)^(1/2)+0.02) = 0 // - 0.16447368*((0.02^2+12.16)^(1/2)+0.02)

x = -(0.16447368*((0.02^2+12.16)^(1/2)+0.02))

x = -0.16447368*((0.02^2+12.16)^(1/2)+0.02)

( x+0.16447368*(0.02-(0.02^2+12.16)^(1/2)) )

x+0.16447368*(0.02-(0.02^2+12.16)^(1/2)) = 0 // - 0.16447368*(0.02-(0.02^2+12.16)^(1/2))

x = -(0.16447368*(0.02-(0.02^2+12.16)^(1/2)))

x = -0.16447368*(0.02-(0.02^2+12.16)^(1/2))

x in { -0.16447368*((0.02^2+12.16)^(1/2)+0.02), -0.16447368*(0.02-(0.02^2+12.16)^(1/2)) }

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