1-8/x-20/x^2=0

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Solution for 1-8/x-20/x^2=0 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)

1-(8/x)-(20/(x^2)) = 0

1-8*x^-1-20*x^-2 = 0

t_1 = x^-1

1-20*t_1^2-8*t_1^1 = 0

1-20*t_1^2-8*t_1 = 0

DELTA = (-8)^2-(-20*1*4)

DELTA = 144

DELTA > 0

t_1 = (144^(1/2)+8)/(-20*2) or t_1 = (8-144^(1/2))/(-20*2)

t_1 = -1/2 or t_1 = 1/10

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

t_1 = 1/10

x^-1-1/10 = 0

1*x^-1 = 1/10 // : 1

x^-1 = 1/10

-1 < 0

1/(x^1) = 1/10 // * x^1

1 = 1/10*x^1 // : 1/10

10 = x^1

x = 10

x in { -2, 10 }

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