Question 74455
Multiplying both sides by t(t+1) gives


{{{62(t+1)=69t+2t(t+1)}}}  or  {{{62t+62=69t+2t^2+2t}}}


Subtracting left side and reordering terms gives


{{{0=2t^2+9t-62}}}


Using quadratic formula gives


{{{t=(-9 +- sqrt(9^2-4*2*(-62)))/(2*2)}}} or {{{t=(-9 +- sqrt(577))/4}}}