9^x^2-1 - 36∗3^x^2-3+3=0

[latex]9^{x^2-1} - 36*3^{x^2-3}+3=0[/latex] [latex](3^2)^{x^2-1} - 36*3^{x^2-3}+3=0[/latex] [latex]3^{2x^2-2} - 36*3^{x^2-3}+3=0[/latex] [latex]3^{2x^2}*3^{-2} - 36*3^{x^2}*3^{-3}+3=0[/latex] [latex]3^{2x^2}* \frac{1}{9} - 36*3^{x^2}* \frac{1}{27} +3=0[/latex] [latex] \frac{1}{9} *3^{2x^2}- \frac{4}{3} *3^{x^2} +3=0[/latex] [latex]3^{x^2}=a[/latex] [latex]\frac{1}{9} a^2- \frac{4}{3} a +3=0[/latex] [latex] a^2- 12a +27=0[/latex] [latex]D=12^2-4*27=144-108=36[/latex] [latex] a_{1} = \frac{12+6}{2} =9[/latex] [latex] a_{2} = \frac{12-6}{2} =3[/latex] [latex]3^{x^2}=9[/latex] [latex]3^{x^2}=3^2[/latex] [latex] x^{2} =2[/latex] [latex]x= \frac{+}{} \sqrt{2} [/latex] [latex]3^{x^2}=3[/latex] [latex]3^{x^2}=3^1[/latex] [latex] x^{2} =1[/latex] [latex]x= \frac{+}{} 1[/latex]