(4/x)+(12/x^2)=5

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Solution for (4/x)+(12/x^2)=5 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)

4/x+12/(x^2) = 5 // - 5

4/x+12/(x^2)-5 = 0

4*x^-1+12*x^-2-5 = 0

t_1 = x^-1

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

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

DELTA = 4^2-(-5*4*12)

DELTA = 256

DELTA > 0

t_1 = (256^(1/2)-4)/(2*12) or t_1 = (-256^(1/2)-4)/(2*12)

t_1 = 1/2 or t_1 = -5/6

t_1 = -5/6

x^-1+5/6 = 0

1*x^-1 = -5/6 // : 1

x^-1 = -5/6

-1 < 0

1/(x^1) = -5/6 // * x^1

1 = -5/6*x^1 // : -5/6

-6/5 = x^1

x = -6/5

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

x in { -6/5, 2 }

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