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

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

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

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

2/(x^2)-5*x^-1-4 = 0

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

t_1 = x^-1

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

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

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

DELTA = 57

DELTA > 0

t_1 = (57^(1/2)+5)/(2*2) or t_1 = (5-57^(1/2))/(2*2)

t_1 = (57^(1/2)+5)/4 or t_1 = (5-57^(1/2))/4

t_1 = (5-57^(1/2))/4

x^-1-((5-57^(1/2))/4) = 0

1*x^-1 = (5-57^(1/2))/4 // : 1

x^-1 = (5-57^(1/2))/4

-1 < 0

1/(x^1) = (5-57^(1/2))/4 // * x^1

1 = ((5-57^(1/2))/4)*x^1 // : (5-57^(1/2))/4

4*(5-57^(1/2))^-1 = x^1

x = 4*(5-57^(1/2))^-1

t_1 = (57^(1/2)+5)/4

x^-1-((57^(1/2)+5)/4) = 0

1*x^-1 = (57^(1/2)+5)/4 // : 1

x^-1 = (57^(1/2)+5)/4

-1 < 0

1/(x^1) = (57^(1/2)+5)/4 // * x^1

1 = ((57^(1/2)+5)/4)*x^1 // : (57^(1/2)+5)/4

4*(57^(1/2)+5)^-1 = x^1

x = 4*(57^(1/2)+5)^-1

x in { 4*(5-57^(1/2))^-1, 4*(57^(1/2)+5)^-1 }

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