`S=2x^2+3y^2-3xy-5x+3y-4`
`=(2x^2-3xy+9/8y^2)-(5x+15/4y)+(15/8y^2-9/4y+3/40)+4-3/40`
`=2(x^2-3/2xy+9/16y^2)-5(x+5/2y)+15/8(y^2-2/5y+1/25)+3 37/40`
`=2[(x-3/4y)^2-2.(x+5/2y).5/4+25/16]+15/8(y-1/5)^2+4/5`
`=2(x-3/4y-5/4)^2+15/8(y-1/5)^2+4/5>=4/5`
`=>A=-(2x^2+3y^2-3xy-5x+3y-4)<=-4/5`
`text{dấu = xảy ra khi}`
$\begin{cases}y=\dfrac{1}{5}\\x=\dfrac{3}{4}y+\dfrac{5}{4}\\\end{cases}$
`<=>`$\begin{cases}y=\dfrac{1}{5}\\x=\dfrac{3}{20}+\dfrac{5}{4}=\dfrac{7}{5}\\\end{cases}$
