6/x^2-43/x=15

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Solution for 6/x^2-43/x=15 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)-(43/x) = 15 // - 15

6/(x^2)-(43/x)-15 = 0

6/(x^2)-43*x^-1-15 = 0

6*x^-2-43*x^-1-15 = 0

t_1 = x^-1

6*t_1^2-43*t_1^1-15 = 0

6*t_1^2-43*t_1-15 = 0

DELTA = (-43)^2-(-15*4*6)

DELTA = 2209

DELTA > 0

t_1 = (2209^(1/2)+43)/(2*6) or t_1 = (43-2209^(1/2))/(2*6)

t_1 = 15/2 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 = 15/2

x^-1-15/2 = 0

1*x^-1 = 15/2 // : 1

x^-1 = 15/2

-1 < 0

1/(x^1) = 15/2 // * x^1

1 = 15/2*x^1 // : 15/2

2/15 = x^1

x = 2/15

x in { -3, 2/15 }

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