6/x^2-37/x=13

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Solution for 6/x^2-37/x=13 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)-(37/x) = 13 // - 13

6/(x^2)-(37/x)-13 = 0

6/(x^2)-37*x^-1-13 = 0

6*x^-2-37*x^-1-13 = 0

t_1 = x^-1

6*t_1^2-37*t_1^1-13 = 0

6*t_1^2-37*t_1-13 = 0

DELTA = (-37)^2-(-13*4*6)

DELTA = 1681

DELTA > 0

t_1 = (1681^(1/2)+37)/(2*6) or t_1 = (37-1681^(1/2))/(2*6)

t_1 = 13/2 or t_1 = -1/3

t_1 = -1/3

x^-1+1/3 = 0

1*x^-1 = -1/3 // : 1

x^-1 = -1/3

-1 < 0

1/(x^1) = -1/3 // * x^1

1 = -1/3*x^1 // : -1/3

-3 = x^1

x = -3

t_1 = 13/2

x^-1-13/2 = 0

1*x^-1 = 13/2 // : 1

x^-1 = 13/2

-1 < 0

1/(x^1) = 13/2 // * x^1

1 = 13/2*x^1 // : 13/2

2/13 = x^1

x = 2/13

x in { -3, 2/13 }

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