![image](https://tex.z-dn.net/?f=%5C%5Clog_%7B%283-2x%29%7D%285x%5E2-10x%2B6%29%3D2%5Ciff+%283-2x%29%5E2%3D5x%5E2-10x%2B6%0A%5C%5C%0A%5C%5C3-2x%3E0+%5C+%5Cwedge+%5C+3-2x%5Cneq1+%5C+%5Cwedge+5x%5E2-10x%2B6%3E0+%5C+%5Cforall+%5C+x%5Cin%5CRe+%5C+%28%5CDelta%3C0%29%0A%5C%5C%0A%5C%5Cx%5Cin%28-%5Cinfty%2C1%29%5Ccup%281%2C1%5Cfrac12%29%0A%5C%5C%0A%5C%5C5x%5E2-10x%2B6%3D4x%5E2-12x%2B9%0A%5C%5C%0A%5C%5Cx%5E2%2B2x-3%3D0%0A%5C%5C%0A%5C%5Cx%5E2-x%2B3x-3%3D0%0A%5C%5C%0A%5C%5Cx%28x-1%29%2B3%28x-1%29%3D0%0A%5C%5C%0A%5C%5C%28x-1%29%28x%2B3%29%3D0%0A%5C%5C%0A%5C%5Cx%3D1%5Cnotin+D+%5C+%5Cvee+x%3D-3%0A%5C%5C%0A%5C%5COTBET%3A+%5C+x%3D-3)
0 \ \wedge \ 3-2x\neq1 \ \wedge 5x^2-10x+6>0 \ \forall \ x\in\Re \ (\Delta<0)
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\\x\in(-\infty,1)\cup(1,1\frac12)
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\\5x^2-10x+6=4x^2-12x+9
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\\x^2+2x-3=0
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\\x^2-x+3x-3=0
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\\x(x-1)+3(x-1)=0
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\\(x-1)(x+3)=0
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\\x=1\notin D \ \vee x=-3
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\\OTBET: \ x=-3" alt="\\log_{(3-2x)}(5x^2-10x+6)=2\iff (3-2x)^2=5x^2-10x+6
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\\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">