Lg(2-3x)+lg(2+3x)=lg(4-x)+lg(x) Помогите!

[latex]lg(2-3x)+lg(2+3x)=lg(4-x)+lgx[/latex] ОДЗ: [latex] \left \{ {{2-3x\ \textgreater \ 0} \atop {2+3x\ \textgreater \ 0}}}} \right.[/latex] [latex] \left \{ {{4-x\ \textgreater \ 0} \atop {x\ \textgreater \ 0}} \right. [/latex] [latex] \left \{ {{x\ \textless \ \frac{2}{3} } \atop {x\ \textgreater \ - \frac{2}{3} }}}} \right. [/latex] [latex] \left \{ {{x\ \textless \ 4} \atop {x\ \textgreater \ 0}} \right. [/latex] [latex]x[/latex] [latex](0; \frac{2}{3} )[/latex] [latex]lg[(2-3x)(2+3x)]=lg[(4-x)x][/latex] [latex]lg(4-9x^2)=lg(4x-x^2)[/latex] [latex]4-9x^2=4x-x^2[/latex] [latex]8x^2+4x-4=0[/latex] [latex]2x^2+x-1=0[/latex] [latex]D=1^2-4*2*(-1)=9[/latex] [latex]x_1= \frac{-1+3}{4}=0.5 [/latex] [latex]x_2= \frac{-1-3}{4}=-1[/latex]  ∅ Ответ: 0.5