(ex-e-x)/2=3,
ex-e-x=6,
e2x-1=6ex,
e2x-6ex-1=0 is a quadratic equation.
e2x-6ex=1,
e2x-6ex+9=10,
(ex-3)2=10,
ex-3=±√10,
ex=3±√10. ex cannot be negative so ex=3+√10 and x=ln(3+√10)=1.8184 approx.
(ex-e-x)/2=3 is the same as sinh(x)=3. x=sinh-1(3) gives the same answer.