Answer
$ln(-2+\sqrt 5)\approx-1.444$
Work Step by Step
Step 1. Let $u=e^{x}$. Multiply both sides of the equation by $u$ and rearrange to get $u^2-1=-4u \longrightarrow u^2+4u-1=0 \longrightarrow u=\frac{-4\pm\sqrt {16+4}}{2}=-2\pm\sqrt 5$
Step 2. For $e^x=-2+\sqrt 5$, we have $x=ln(-2+\sqrt 5)\approx-1.444$
Step 3. For $e^x=-2-\sqrt 5\lt0$, there is no real solution.
Step 4. Check, $x=ln(-2+\sqrt 5)\approx-1.444$ fits the original equation.
