2x^2-5/x=51

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Solution for 2x^2-5/x=51 equation:


D( x )

x = 0

x = 0

x = 0

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

2*x^2-(5/x) = 51 // - 51

2*x^2-(5/x)-51 = 0

2*x^2-5*x^-1-51 = 0

2*x^2-5*x^-1-51*x^0 = 0

(2*x^3-51*x^1-5*x^0)/(x^1) = 0 // * x^2

x^1*(2*x^3-51*x^1-5*x^0) = 0

x^1

2*x^3-51*x-5 = 0

{ 1, -1, 5, -5 }

1

x = 1

2*x^3-51*x-5 = -54

1

-1

x = -1

2*x^3-51*x-5 = 44

-1

5

x = 5

2*x^3-51*x-5 = -10

5

-5

x = -5

2*x^3-51*x-5 = 0

-5

x+5

2*x^2-10*x-1

2*x^3-51*x-5

x+5

-2*x^3-10*x^2

-10*x^2-51*x-5

10*x^2+50*x

-x-5

x+5

0

2*x^2-10*x-1 = 0

DELTA = (-10)^2-(-1*2*4)

DELTA = 108

DELTA > 0

x = (108^(1/2)+10)/(2*2) or x = (10-108^(1/2))/(2*2)

x = (6*3^(1/2)+10)/4 or x = (10-6*3^(1/2))/4

x in { (10-6*3^(1/2))/4, (6*3^(1/2)+10)/4, -5}

x in { (10-6*3^(1/2))/4, (6*3^(1/2)+10)/4, -5 }

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