How to solve $\frac{3}{2}x-\frac{4}{5}=\sqrt{\sin(30^\circ)+\sin\frac{7\pi}{4}}$ I did it as: $$\Bigl(\frac{3}{2}x-\frac{4}{5}\Bigr)^2=\Biggl(\sqrt{\frac{1}{2}-\frac{\sqrt{2}}{2}}\Biggr)^2.$$ But after, got big numbers $$225x^2-63-\sqrt{2}=0.$$ It would be very good, if someone showed the correct way of solving this. It must be solved in $\Bbb R.$

$$\frac{3}{2}x-\frac{4}{5}=\sqrt{\frac{1}{2}-\frac{1}{\sqrt2}},$$
which is impossible because $\frac{1}{2}-\frac{1}{\sqrt2}<0$.
The answer is $\oslash$
