\(P=2x^2+3x\)
\(P=5\)
\(\Leftrightarrow2x^2+3x=5\)
\(\Leftrightarrow2x^2+3x-5=0\)
\(\Leftrightarrow2x^2-2x+5x-5=0\)
\(\Leftrightarrow2x\left(x-1\right)+5\left(x-1\right)=0\)
\(\Leftrightarrow\left(2x+5\right)\left(x-1\right)=0\)
\(\Rightarrow\orbr{\begin{cases}2x+5=0\\x-1=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{-5}{2}\\x=1\end{cases}}\)
\(2x^2+3x=5\)
\(2x^2+3x-5=0\)
\(x^2+\frac{3}{2}x-\frac{5}{2}=0\)
\(x^2+2.\frac{3}{4}x+\frac{9}{16}-\frac{9}{16}-\frac{5}{2}=0\)
\(\left(x+\frac{3}{4}\right)^2-\frac{49}{16}=0\)
\(\left(x+\frac{3}{4}-\frac{7}{4}\right)\left(x+\frac{3}{4}+\frac{7}{4}\right)=0\)
\(\left(x-1\right)\left(x+\frac{5}{2}\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x-1=0\\x+\frac{5}{2}=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=1\\x=\frac{-5}{2}\end{cases}}\)
