Answer
no real solution.
Work Step by Step
Step 1. Let $u=7^x$, we have $2u^2+11u+5=0 \longrightarrow (2u+1)(u+5)=0 \longrightarrow u=-5,-\frac{1}{2}$
Step 2. For $u=-5$, we have $7^x=-5 \longrightarrow $ no real solution.
Step 3. For $u=-\frac{1}{2}$, we have $7^x=-\frac{1}{2} \longrightarrow $ no real solution.
