6/x^2-9/x=4/3

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Solution for 6/x^2-9/x=4/3 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)

6/(x^2)-(9/x) = 4/3 // - 4/3

6/(x^2)-(9/x)-(4/3) = 0

6/(x^2)-9*x^-1-4/3 = 0

6*x^-2-9*x^-1-4/3 = 0

t_1 = x^-1

6*t_1^2-9*t_1^1-4/3 = 0

6*t_1^2-9*t_1-4/3 = 0

DELTA = (-9)^2-(-4/3*4*6)

DELTA = 113

DELTA > 0

t_1 = (113^(1/2)+9)/(2*6) or t_1 = (9-113^(1/2))/(2*6)

t_1 = (113^(1/2)+9)/12 or t_1 = (9-113^(1/2))/12

t_1 = (9-113^(1/2))/12

x^-1-((9-113^(1/2))/12) = 0

1*x^-1 = (9-113^(1/2))/12 // : 1

x^-1 = (9-113^(1/2))/12

-1 < 0

1/(x^1) = (9-113^(1/2))/12 // * x^1

1 = ((9-113^(1/2))/12)*x^1 // : (9-113^(1/2))/12

12*(9-113^(1/2))^-1 = x^1

x = 12*(9-113^(1/2))^-1

t_1 = (113^(1/2)+9)/12

x^-1-((113^(1/2)+9)/12) = 0

1*x^-1 = (113^(1/2)+9)/12 // : 1

x^-1 = (113^(1/2)+9)/12

-1 < 0

1/(x^1) = (113^(1/2)+9)/12 // * x^1

1 = ((113^(1/2)+9)/12)*x^1 // : (113^(1/2)+9)/12

12*(113^(1/2)+9)^-1 = x^1

x = 12*(113^(1/2)+9)^-1

x in { 12*(9-113^(1/2))^-1, 12*(113^(1/2)+9)^-1 }

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