20/x^2-1/x=1

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

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

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

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

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

t_1 = x^-1

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

20*t_1^2-t_1-1 = 0

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

DELTA = 81

DELTA > 0

t_1 = (81^(1/2)+1)/(2*20) or t_1 = (1-81^(1/2))/(2*20)

t_1 = 1/4 or t_1 = -1/5

t_1 = -1/5

x^-1+1/5 = 0

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

x^-1 = -1/5

-1 < 0

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

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

-5 = x^1

x = -5

t_1 = 1/4

x^-1-1/4 = 0

1*x^-1 = 1/4 // : 1

x^-1 = 1/4

-1 < 0

1/(x^1) = 1/4 // * x^1

1 = 1/4*x^1 // : 1/4

4 = x^1

x = 4

x in { -5, 4 }