(5/x^2)-(43/x)=18

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Solution for (5/x^2)-(43/x)=18 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)

5/(x^2)-(43/x) = 18 // - 18

5/(x^2)-(43/x)-18 = 0

5/(x^2)-43*x^-1-18 = 0

5*x^-2-43*x^-1-18 = 0

t_1 = x^-1

5*t_1^2-43*t_1^1-18 = 0

5*t_1^2-43*t_1-18 = 0

DELTA = (-43)^2-(-18*4*5)

DELTA = 2209

DELTA > 0

t_1 = (2209^(1/2)+43)/(2*5) or t_1 = (43-2209^(1/2))/(2*5)

t_1 = 9 or t_1 = -2/5

t_1 = -2/5

x^-1+2/5 = 0

1*x^-1 = -2/5 // : 1

x^-1 = -2/5

-1 < 0

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

1 = -2/5*x^1 // : -2/5

-5/2 = x^1

x = -5/2

t_1 = 9

x^-1-9 = 0

1*x^-1 = 9 // : 1

x^-1 = 9

-1 < 0

1/(x^1) = 9 // * x^1

1 = 9*x^1 // : 9

1/9 = x^1

x = 1/9

x in { -5/2, 1/9 }

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