Lorentz formula $$t' =\frac{t-vx/c^2}{\sqrt{1-v^2/c^2}} = t\sqrt{\frac{1-v/c}{1+v/c}}$$ if x=ct.
And equalities x=ct and x'=ct' are the base conditions for Lorentz formula derivation.
So, equation $$t' =t\sqrt{\frac{1-v/c}{1+v/c}}$$ is quite right Lorentz formula,
Value t' is the time in the...