2/x^2-5/x+2=0

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Solution for 2/x^2-5/x+2=0 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)+2 = 0

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

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

t_1 = x^-1

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

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

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

DELTA = 9

DELTA > 0

t_1 = (9^(1/2)+5)/(2*2) or t_1 = (5-9^(1/2))/(2*2)

t_1 = 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 = 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 { 2, 1/2 }

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