Question 358754
I don't think there is a standard closed form solution, unless you're interested in the Lambert W function and then,
{{{highlight(x=-W(4)/2)}}}
.
.
.
I solved it using Newton's method.
f(x)={{{x+ 2e^(2x)}}}
f'(x)={{{1+4x^(2x)}}}
{{{highlight(x=-0.60108)}}}