(3/t^2)-(12/t)+9=0

Solution for (3/t^2)-(12/t)+9=0 equation:

D( t )

t^2 = 0

t = 0

t^2 = 0

t^2 = 0

1*t^2 = 0 // : 1

t^2 = 0

t = 0

t = 0

t = 0

t in (-oo:0) U (0:+oo)

3/(t^2)-(12/t)+9 = 0

3/(t^2)-12*t^-1+9 = 0

3*t^-2-12*t^-1+9 = 0

t_1 = t^-1

3*t_1^2-12*t_1^1+9 = 0

3*t_1^2-12*t_1+9 = 0

DELTA = (-12)^2-(3*4*9)

DELTA = 36

DELTA > 0

t_1 = (36^(1/2)+12)/(2*3) or t_1 = (12-36^(1/2))/(2*3)

t_1 = 3 or t_1 = 1

t_1 = 1

t^-1-1 = 0

1*t^-1 = 1 // : 1

t^-1 = 1

-1 < 0

1/(t^1) = 1 // * t^1

1 = 1*t^1 // : 1

1 = t^1

t = 1

t_1 = 3

t^-1-3 = 0

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

t^-1 = 3

-1 < 0

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

1 = 3*t^1 // : 3

1/3 = t^1

t = 1/3

t in { 1, 1/3 }