0 = 1 − 4 e t + e ( 2 t ) {\displaystyle 0=1-4e^{t}+e^{(2t)}}
Substitution x = e t {\displaystyle x=e^{t}}
0 = 1 − 4 x + x 2 {\displaystyle 0=1-4x+x^{2}}
x = 2 + − 3 {\displaystyle x=2+-{\sqrt {3}}}
e t = 2 + − 3 {\displaystyle e^{t}=2+-{\sqrt {3}}}
t = l n ( 2 + − 3 ) {\displaystyle t=ln(2+-{\sqrt {3}})}