1+1/x=42/x^2

Solution for 1+1/x=42/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)

1/x+1 = 42/(x^2) // - 42/(x^2)

1/x-(42/(x^2))+1 = 0

1/x-42*x^-2+1 = 0

x^-1-42*x^-2+1 = 0

t_1 = x^-1

1*t_1^1-42*t_1^2+1 = 0

t_1-42*t_1^2+1 = 0

DELTA = 1^2-(-42*1*4)

DELTA = 169

DELTA > 0

t_1 = (169^(1/2)-1)/(-42*2) or t_1 = (-169^(1/2)-1)/(-42*2)

t_1 = -1/7 or t_1 = 1/6

t_1 = -1/7

x^-1+1/7 = 0

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

x^-1 = -1/7

-1 < 0

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

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

-7 = x^1

x = -7

t_1 = 1/6

x^-1-1/6 = 0

1*x^-1 = 1/6 // : 1

x^-1 = 1/6

-1 < 0

1/(x^1) = 1/6 // * x^1

1 = 1/6*x^1 // : 1/6

6 = x^1

x = 6

x in { -7, 6 }