Question 607249
{{{8t/(t^2+3)=2}}}.....both sides multiply by {{{t^2+3}}}

{{{(8t/(t^2+3))(t^2+3)=2(t^2+3)}}}

{{{(8t/cross((t^2+3)))cross((t^2+3))=2(t^2+3)}}}

{{{8t=2t^2+6}}}

{{{8t-8t=2t^2-8t+6}}}

{{{0=2t^2-8t+6}}}.......or.....{{{2t^2-8t+6=0}}}.....solve for {{{t}}} using quadratic formula

{{{t = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}...note that {{{a=2}}}, {{{b=-8}}} and {{{c=6}}}

{{{t = (-(-8) +- sqrt((-8)^2-4*2*6 ))/(2*2) }}}

{{{t = (8 +- sqrt(64-48 ))/4 }}}

{{{t = (8 +- sqrt(16))/4 }}}

{{{t = (8 +- 4)/4 }}}

solutions:

{{{t = (8 +4)/4 }}}

{{{t = 12/4 }}}

{{{t = 3 }}}

or

{{{t = (8 -4)/4 }}}

{{{t = 4/4 }}}

{{{t = 1 }}}