$7.5 \quad 7^{x}(\sqrt{2})^{2 x^{2}-6}-\left(\frac{7}{4}\right)^{x}=0$.
7.5 Instruction. Divide both sides of the equation by the positive number $\left(\frac{7}{4}\right)^{x}$.

Omвem: $x_{1}=-3, x_{2}=1$.