144t^2+1/t^2+24

Solution for 144t^2+1/t^2+24 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)

144*t^2+1/(t^2)+24 = 0

144*t^2+t^-2+24 = 0

t_1 = t^2

144*t_1^1+1*t_1^-1+24 = 0

144*t_1^1+1*t_1^-1+24*t_1^0 = 0

(144*t_1^2+24*t_1^1+1*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(144*t_1^2+24*t_1^1+1*t_1^0) = 0

t_1^1

144*t_1^2+24*t_1+1 = 0

144*t_1^2+24*t_1+1 = 0

DELTA = 24^2-(1*4*144)

DELTA = 0

t_1 = -24/(2*144)

t_1 = -1/12 or t_1 = -1/12

t_1 in { -1/12, -1/12} 

t_1 = -1/12

t^2+1/12 = 0

1*t^2 = -1/12 // : 1

t^2 = -1/12

t_1 = -1/12

t^2+1/12 = 0

1*t^2 = -1/12 // : 1

t^2 = -1/12

t belongs to the empty set