21-(1/x)=(2/x^2)

Solution for 21-(1/x)=(2/x^2) 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)

21-(1/x) = 2/(x^2) // - 2/(x^2)

21-(1/x)-(2/(x^2)) = 0

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

t_1 = x^-1

21-2*t_1^2-1*t_1^1 = 0

21-2*t_1^2-t_1 = 0

DELTA = (-1)^2-(-2*4*21)

DELTA = 169

DELTA > 0

t_1 = (169^(1/2)+1)/(-2*2) or t_1 = (1-169^(1/2))/(-2*2)

t_1 = -7/2 or t_1 = 3

t_1 = -7/2

x^-1+7/2 = 0

1*x^-1 = -7/2 // : 1

x^-1 = -7/2

-1 < 0

1/(x^1) = -7/2 // * x^1

1 = -7/2*x^1 // : -7/2

-2/7 = x^1

x = -2/7

t_1 = 3

x^-1-3 = 0

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

x^-1 = 3

-1 < 0

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

1 = 3*x^1 // : 3

1/3 = x^1

x = 1/3

x in { -2/7, 1/3 }