Hello!
The answer is:
[tex]3x^{2} -14x+7[/tex]
Why?
To solve the problem we need to add/subtract like terms. We need to remember that like terms are the terms that share the same variable and the same exponent.
For example, we have:
[tex]x^{2} +2x+3x=x^{2} +(2x+3x)=x^{2}+5x[/tex]
We have that we were able to add just the terms that were sharing the same variable and exponenr (x for this case).
So, we are given the expression:
[tex]5x^2-5x+1-(2x^2+9x-6)=5x^{2}-2x^{2}-5x-9x+1-(-6)\\\\(5x^{2}-2x^{2})+(-5x-9x)+(1-(-6))=3x^{2}-14x+7[/tex]
Hence, the answer is:
[tex]3x^{2} -14x+7[/tex]
Have a nice day!
