Let $f$ be a function satisfying $2f\left(x\right)-3f(1/x)=x^2$ for any $x\ne 0.$ Then the value of $f\left(2\right)$ is 

$\begin{array}{l}2f\left(2\right)-3f(1/2)=2^2=4\to \left(1\right)\\ 2f(1/2)-3f\left(2\right)=(1/2{)}^2=1/4\\ \Rightarrow 5\left(f\right(2)-f(1/2\left)\right)=4-1/4=15/4\\ \Rightarrow f(1/2)=f\left(2\right)-3/4.\end{array}$

So $\begin{array}{r} 2f\left(2\right)-3\left[f\right(2)-3/4]=4(\because from (1\left)\right)\\ \Rightarrow f\left(2\right)=\frac{9}{4}-4=-\frac{7}{4}\end{array}$