\(\displaystyle{\left({3}{x}^{{2}}+{2}{x}-{1}\right)}-{\left(-{5}{x}^{{2}}+{8}{x}+{4}\right)}\)

\(\displaystyle={\left({3}{x}^{{2}}+{2}{x}-{1}\right)}+{\left({5}{x}^{{2}}-{8}{x}-{4}\right)}\)

\(\displaystyle={3}{x}^{{2}}+{5}{x}^{{2}}+{2}{x}-{8}{x}-{1}-{4}\)

\(\displaystyle={\left({3}+{5}\right)}{x}^{{2}}+{\left({2}-{8}\right)}{x}-{5}\)

\(\displaystyle={8}{x}^{{2}}-{6}{x}-{5}\)

Hence, the solution is \(\displaystyle{8}{x}^{{2}}-{6}{x}-{5}\)