3-16/x-12/x^2=0

Solution for 3-16/x-12/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)

3-(16/x)-(12/(x^2)) = 0

3-16*x^-1-12*x^-2 = 0

t_1 = x^-1

3-12*t_1^2-16*t_1^1 = 0

3-12*t_1^2-16*t_1 = 0

DELTA = (-16)^2-(-12*3*4)

DELTA = 400

DELTA > 0

t_1 = (400^(1/2)+16)/(-12*2) or t_1 = (16-400^(1/2))/(-12*2)

t_1 = -3/2 or t_1 = 1/6

t_1 = -3/2

x^-1+3/2 = 0

1*x^-1 = -3/2 // : 1

x^-1 = -3/2

-1 < 0

1/(x^1) = -3/2 // * x^1

1 = -3/2*x^1 // : -3/2

-2/3 = x^1

x = -2/3

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 { -2/3, 6 }