[tex]\displaystyle{ 3^{37} - 27^{12} = 2 \cdot 81^{10} : x^{2} }[/tex]
[tex]\displaystyle{ 3^{37} - (3^{3})^{12} = 2 \cdot (3^{4})^{10} : x^{2} }[/tex]
[tex]\displaystyle{ 3^{37} - 3^{36} = 2 \cdot 3^{40} : x^{2} }[/tex]
[tex]\displaystyle{ x^{2} = 2 \cdot 3^{40} : (3^{37} - 3^{36}) }[/tex]
[tex]\displaystyle{ x^{2} = 2 \cdot 3^{40} : 3^{36} \cdot (3 - 1) }[/tex]
[tex]\displaystyle{ x^{2} = 2 \cdot 3^{40-36} \cdot 2 }[/tex]
[tex]\displaystyle{ x^{2} = 2 \cdot 3^{4} \cdot 2 }[/tex]
[tex]\displaystyle{ x^{2} = 4 \cdot 81 }[/tex]
[tex]\displaystyle{ x = \sqrt{4} \cdot \sqrt{81} }[/tex]
[tex]\displaystyle{ x = 2 \cdot 9 }[/tex]
[tex]\boxed{x=18}[/tex]
