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[latex]7.\;x^2-3x\ \textless \ -m\\x^2-3x+m\ \textless \ 0\\x^2-3x+m=0\\D=9-4m\\x_{1}=\frac{3-\sqrt{9-4m}}2\\x_2=\frac{3+\sqrt{9-4m}}2\\x_1=-1,\;x_2=4\\\begin{cases}\frac{3-\sqrt{9-4m}}2=-1\\\frac{3+\sqrt{9-4m}}2=4\end{cases}\Rightarrow\begin{cases}3-\sqrt{9-4m}=-2\\3+\sqrt{9-4m}=8\end{cases}\Rightarrow\begin{cases}\sqrt{9-4m}=5\\\sqrt{9-4m}=5\end{cases}\\\sqrt{9-4m}=5\\9-4m=25\\4m=-16\\m=-4\\\\8.\;y=\sqrt{1-6x+5x^2}\\1-6x+5x^2\geq0\\5x^2-6x+1=0\\D=36-4\cdot5=16\\x_1=1,\;x_2=5\\5(x-\frac15)(x-5)\geq0[/latex] [latex]x\in\left(-\infty;\;\frac15\right)\cup\left(5;\;+\infty\right)[/latex] [latex]9.\;ax^2+16x=-4a\\ax^2+16x+4a=0\\D=256-16a^2\\256-16a^2\ \textless \ 0\\16a^2\ \textgreater \ 256\\a^2\ \textgreater \ 16\\a\in(-\infty;\;-4)\cup(4;\;+\infty)\\\\10.\;\begin{cases}xy-(x+y)=x-y\\xy-(x+y)=7\end{cases}\Rightarrow\begin{cases}xy-(x+y)=x-y\\x-y=7\end{cases}\Rightarrow\\\Rightarrow\begin{cases}x(x-7)-(x+x-7)=x-(x-7)\\y=x-7\end{cases}\\x(x-7)-(x+x-7)=x-(x-7)\\x^2-7x-2x+7=7\\x^2-9x=0\\x(x-9)=0\\x_1=0,\;x_2=9\\\begin{cases}x_1=0\\y_1=-7\end{cases}\quad\quad u\quad\quad\;\;\begin{cases}x_2=9\\y_2=2\end{cases}[/latex]