4t^2+1/t^2+4=0

Solution for 4t^2+1/t^2+4=0 equation:

D( t )

t^2 = 0

t^2 = 0

t^2 = 0

1*t^2 = 0 // : 1

t^2 = 0

t = 0

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

4*t^2+1/(t^2)+4 = 0

4*t^2+t^-2+4 = 0

t_1 = t^2

4*t_1^1+1*t_1^-1+4 = 0

4*t_1^1+1*t_1^-1+4*t_1^0 = 0

(4*t_1^2+4*t_1^1+1*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(4*t_1^2+4*t_1^1+1*t_1^0) = 0

t_1^1

4*t_1^2+4*t_1+1 = 0

4*t_1^2+4*t_1+1 = 0

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

DELTA = 0

t_1 = -4/(2*4)

t_1 = -1/2 or t_1 = -1/2

t_1 in { -1/2, -1/2} 

t_1 = -1/2

t^2+1/2 = 0

1*t^2 = -1/2 // : 1

t^2 = -1/2

t_1 = -1/2

t^2+1/2 = 0

1*t^2 = -1/2 // : 1

t^2 = -1/2

t belongs to the empty set