1/t+1/2t+1/3t=5

Solution for 1/t+1/2t+1/3t=5 equation:

D( t )

t = 0

t = 0

t = 0

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

(1/2)*t+(1/3)*t+1/t = 5 // - 5

(1/2)*t+(1/3)*t+1/t-5 = 0

5/6*t^1+1*t^-1-5*t^0 = 0

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

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

t^1

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

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

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

DELTA = 65/3

DELTA > 0

t = ((65/3)^(1/2)+5)/(2*(5/6)) or t = (5-(65/3)^(1/2))/(2*(5/6))

t = 3/5*((65/3)^(1/2)+5) or t = 3/5*(5-(65/3)^(1/2))

t in { 3/5*(5-(65/3)^(1/2)), 3/5*((65/3)^(1/2)+5)} 

t in { 3/5*(5-(65/3)^(1/2)), 3/5*((65/3)^(1/2)+5) }