5/x=4/x^2-6

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Solution for 5/x=4/x^2-6 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)

5/x = 4/(x^2)-6 // - 4/(x^2)-6

5/x-(4/(x^2))+6 = 0

5/x-4*x^-2+6 = 0

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

t_1 = x^-1

5*t_1^1-4*t_1^2+6 = 0

5*t_1-4*t_1^2+6 = 0

DELTA = 5^2-(-4*4*6)

DELTA = 121

DELTA > 0

t_1 = (121^(1/2)-5)/(-4*2) or t_1 = (-121^(1/2)-5)/(-4*2)

t_1 = -3/4 or t_1 = 2

t_1 = -3/4

x^-1+3/4 = 0

1*x^-1 = -3/4 // : 1

x^-1 = -3/4

-1 < 0

1/(x^1) = -3/4 // * x^1

1 = -3/4*x^1 // : -3/4

-4/3 = x^1

x = -4/3

t_1 = 2

x^-1-2 = 0

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

x^-1 = 2

-1 < 0

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

1 = 2*x^1 // : 2

1/2 = x^1

x = 1/2

x in { -4/3, 1/2 }

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