Question 756620
We cannot solve for t from what was posted.
There is no equal sign, so there is no equation that would give any information about t.
 
EXAMPLES:
7t/(a-t) = (a+t)/7t and 7t/a-t = a+t/7t
are equations because each one has an equal sign.
They can be solved for t, and I will show you how I would solve them.
NOTE:
Those parentheses make a big difference in the meaning of the expressions on both sides of the equal sign.
With pencil and paper, I can easily write 
7t/(a-t) = (a+t)/7t as {{{7t/(a-t) = (a+t)/7t}}}.
Those long horizontal fraction lines above {{{a-t}}} and below {{{a+t}}} include invisible parentheses wrapping everything written above the line, and everything written below the line.
 
7t/a-t = a+t/7t can be written as {{{7t/a-t = a+t/7t}}}
which can be simplified to {{{7t/a-t = a+1/7}}}
I don't like equations with fractions, so at this time, I would multiply everything times 7. That gives me the equivalent equation
{{{49t/a-7t = 7a+1}}}
Taking out common factor t, we get
{{{(49/a-7)t = 7a+1}}} --> {{{(49/a-7a/a)t = 7a+1}}} --> {{{((49-7a)/a)t = 7a+1}}}
Finally, we get the solution by multiplying both sides of the equal sign times {{{a/(49-7a)}}}, which is the same as dividing by {{{(49-7a)/a}}}
{{{((49-7a)/a)t=7a+1}}} --> {{{((49-7a)/a)((49-7a)/a)t = ((49-7a)/a)7a+1}}} --> {{{t=(7a+1)(49-7a)/a}}} --> {{{t=(343a-49a^2+49-7a)/a}}} --> {{{t=(49+336a-49a^2)/a}}}
 
7t/(a-t) = (a+t)/7t can be written as {{{7t/(a-t) = (a+t)/7t}}}
Multiplying oth sides of the equal sign times {{{7t}}} we get
{{{49t^2/(a-t) = (a+t)7t/7t}}} --> {{{49t^2/(a-t)=a+t}}}
Next, multiplying oth sides of the equal sign times {{{(a-t)}}} we get
{{{49t^2(a-t)/(a-t)=(a+t)(a-t)}}} --> {{{49t^2=a^2-t^2}}}
Now, adding {{{t^2}}} to both sides of the equation, we get
{{{50t^2=a^2}}} --> {{{t^2=a^2/50}}}
There are two solutions to that equation.
One is {{{t=a/sqrt(50)}}} and it can be written more elegantlu as {{{t=a*sqrt(2)/5}}}.
The other solution is {{{t=-a/sqrt(50)}}} , which can be written more elegantly as {{{t=-a*sqrt(2)/5}}}.