7.068. $2^{x^{2}-1}-3^{x^{2}}=3^{x^{2}-1}-2^{x^{2}+2}$.
## Solution.

We have $\frac{2^{x^{2}}}{2}+4 \cdot 2^{x^{2}}=\frac{3^{x^{2}}}{3}+3^{x^{2}}, \frac{9}{2} \cdot 2^{x^{2}}=\frac{4}{3} \cdot 3^{x^{2}},\left(\frac{2}{3}\right)^{x^{2}}=\left(\frac{2}{3}\right)^{3}$.

Then $x^{2}=3$, from which $x_{1}=-\sqrt{3}, x_{2}=\sqrt{3}$.

Answer: $-\sqrt{3} ; \sqrt{3}$.