From the sum of $$3x^{2} - 5x + 2$$ and $$-5x^{2} - 8x + 9$$ subtract $$4x^{2} - 7x + 9$$.
Let us add $$3x^2-5x+2$$ ad $$-5x^2-8x+9$$ first,
$$\begin{array}{l}\left( {3{x^2} - 5x + 2} \right) + \left( { - 5{x^2} - 8x + 9} \right)\\ \Rightarrow \left( {3{x^2} - 5{x^2}} \right) + \left( { - 5x - 8x} \right) + \left( {2 + 9} \right)\\ \Rightarrow - 2{x^2} - 13x + 11\end{array}$$
Now, we will subtract $$4x^2-7x+9$$ from the above-obtained result,
$$\begin{array}{l}\left( { - 2{x^2} - 13x + 11} \right) - \left( {4{x^2} - 7x + 9} \right)\\ \Rightarrow - 2{x^2} - 13x + 11 - 4{x^2} + 7x - 9\\ \Rightarrow \left( { - 2{x^2} - 4{x^2}} \right) + \left( { - 13x + 7x} \right) + \left( {11 - 9} \right)\\ \Rightarrow - 6{x^2} - 6x + 2\end{array}$$