4+x+3/4=17/2
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\(4\left(x+2\right)=3\left(x+1\right)+17\)
\(4x+8=3x+3+17\)
\(4x-3x=3+17-8\)
\(x=12\)

\(4\left(2x-1\right)^3-17=10^2-3^2\)
\(\Rightarrow4\left(2x-1\right)^3-17=100-9\)
\(\Rightarrow4\left(2x-1\right)^3-17=91\)
\(\Rightarrow4\left(2x-1\right)^3=91+17\)
\(\Rightarrow4\left(2x-1\right)^3=108\)
\(\Rightarrow\left(2x-1\right)^3=108:4\)
\(\Rightarrow\left(2x-1\right)^3=27\)
\(\Rightarrow\left(2x-1\right)^3=3^3\)
\(\Rightarrow2x-1=3\)
\(\Rightarrow2x=3+1\)
\(\Rightarrow2x=4\)
\(\Rightarrow x=4:2\)
\(\Rightarrow x=2\)
=>4(2x-1)^3=100-9+17=108
=>(2x-1)^3=27
=>2x-1=3
=>2x=4
=>x=2

\(\Rightarrow x^3-3x^2+3x-1+8-x^3=17-3x^2-6x\\ \Rightarrow9x=10\Rightarrow x=\dfrac{10}{9}\)

a) \(\left(x+3\right)\left(2x-1\right)-\left(x-3\right)\left(x+1\right)=0\)
\(\Leftrightarrow2x^2+5x-3-x^2+2x+3=0\)
\(\Leftrightarrow x^2+7x=0\Leftrightarrow x\left(x+7\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-7\end{matrix}\right.\)
b) \(\left(x+4\right)\left(2x-3\right)-3\left(x-2\right)\left(x+2\right)=0\)
\(\Leftrightarrow2x^2+5x-12-3x^2+12=0\)
\(\Leftrightarrow x^2-5x=0\Leftrightarrow x\left(x-5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=5\end{matrix}\right.\)
4 + \(x+\frac34\) = \(\frac{17}{2}\)
4 + \(x\) = \(\frac{17}{2}\) - \(\frac34\)
4 + \(x\) = \(\frac{34}{4}\) - \(\frac34\)
4 + \(x\) = \(\frac{31}{4}\)
\(x=\frac{31}{4}-4\)
\(x\) = \(\frac{31}{4}-\frac{16}{4}\)
\(x\) = \(\frac{15}{4}\)
x = 34/4 - 16/4 - 3/4
x = (34 - 16 - 3)/4
x = 15/4
Vậy x = 15/4.