$\left(3 x^{2}+2 x\right)-\left(8 x^{2}+7\right)$

Step 1 ：Given the polynomials \(3 x^{2}+2 x\) and \(8 x^{2}+7\)

Step 2 ：We are asked to subtract the second polynomial from the first

Step 3 ：To do this, we subtract the like terms separately

Step 4 ：Subtracting the coefficients of \(x^{2}\) terms gives us \(-5x^{2}\)

Step 5 ：Subtracting the constant terms gives us \(-7\)

Step 6 ：The term \(2x\) remains unchanged as there is no corresponding term in the second polynomial

Step 7 ：So, the result of the subtraction is \(-5x^{2} + 2x - 7\)

Step 8 ：Final Answer: \(\boxed{-5x^{2} + 2x - 7}\)