8/x^2=8/x+6

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Solution for 8/x^2=8/x+6 equation: 


D( x )

x = 0

x^2 = 0

x = 0

x = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

8/(x^2) = 8/x+6 // - 8/x+6

8/(x^2)-(8/x)-6 = 0

8/(x^2)-8*x^-1-6 = 0

8*x^-2-8*x^-1-6 = 0

t_1 = x^-1

8*t_1^2-8*t_1^1-6 = 0

8*t_1^2-8*t_1-6 = 0

DELTA = (-8)^2-(-6*4*8)

DELTA = 256

DELTA > 0

t_1 = (256^(1/2)+8)/(2*8) or t_1 = (8-256^(1/2))/(2*8)

t_1 = 3/2 or t_1 = -1/2

t_1 = -1/2

x^-1+1/2 = 0

1*x^-1 = -1/2 // : 1

x^-1 = -1/2

-1 < 0

1/(x^1) = -1/2 // * x^1

1 = -1/2*x^1 // : -1/2

-2 = x^1

x = -2

t_1 = 3/2

x^-1-3/2 = 0

1*x^-1 = 3/2 // : 1

x^-1 = 3/2

-1 < 0

1/(x^1) = 3/2 // * x^1

1 = 3/2*x^1 // : 3/2

2/3 = x^1

x = 2/3

x in { -2, 2/3 }

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