6-1/t-5/t^2=0

Solution for 6-1/t-5/t^2=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)

6-(1/t)-(5/(t^2)) = 0

6-t^-1-5*t^-2 = 0

t_1 = t^-1

6-5*t_1^2-1*t_1^1 = 0

6-5*t_1^2-t_1 = 0

DELTA = (-1)^2-(-5*4*6)

DELTA = 121

DELTA > 0

t_1 = (121^(1/2)+1)/(-5*2) or t_1 = (1-121^(1/2))/(-5*2)

t_1 = -6/5 or t_1 = 1

t_1 = -6/5

t^-1+6/5 = 0

1*t^-1 = -6/5 // : 1

t^-1 = -6/5

-1 < 0

1/(t^1) = -6/5 // * t^1

1 = -6/5*t^1 // : -6/5

-5/6 = t^1

t = -5/6

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 in { -5/6, 1 }