no. and nature of roots of ${x}^{\frac{3}{4}({\mathrm{log}}_{2}x{)}^{2}+{\mathrm{log}}_{2}x-\frac{5}{4}}=\sqrt{2}$

The given equation is

${x}^{\frac{3}{4}({\mathrm{log}}_{2}x{)}^{2}+{\mathrm{log}}_{2}x-\frac{5}{4}}=\sqrt{2}$

I took ${\mathrm{log}}_{2}x$

and then rewrote the given equation as

${x}^{3{t}^{2}+4t-5}=\sqrt{2}$

But I don't know what to do after this. How will I find the nature and no. of roots?

The given equation is

${x}^{\frac{3}{4}({\mathrm{log}}_{2}x{)}^{2}+{\mathrm{log}}_{2}x-\frac{5}{4}}=\sqrt{2}$

I took ${\mathrm{log}}_{2}x$

and then rewrote the given equation as

${x}^{3{t}^{2}+4t-5}=\sqrt{2}$

But I don't know what to do after this. How will I find the nature and no. of roots?