0 \ \wedge \ 3-2x\neq1 \ \wedge 5x^2-10x+6>0 \ \forall \ x\in\Re \ (\Delta<0)
\\
\\x\in(-\infty,1)\cup(1,1\frac12)
\\
\\5x^2-10x+6=4x^2-12x+9
\\
\\x^2+2x-3=0
\\
\\x^2-x+3x-3=0
\\
\\x(x-1)+3(x-1)=0
\\
\\(x-1)(x+3)=0
\\
\\x=1\notin D \ \vee x=-3
\\
\\OTBET: \ x=-3" alt="\\log_{(3-2x)}(5x^2-10x+6)=2\iff (3-2x)^2=5x^2-10x+6
\\
\\3-2x>0 \ \wedge \ 3-2x\neq1 \ \wedge 5x^2-10x+6>0 \ \forall \ x\in\Re \ (\Delta<0)
\\
\\x\in(-\infty,1)\cup(1,1\frac12)
\\
\\5x^2-10x+6=4x^2-12x+9
\\
\\x^2+2x-3=0
\\
\\x^2-x+3x-3=0
\\
\\x(x-1)+3(x-1)=0
\\
\\(x-1)(x+3)=0
\\
\\x=1\notin D \ \vee x=-3
\\
\\OTBET: \ x=-3" align="absmiddle" class="latex-formula">