[tex]1.) \frac{2}{3}x^{2}+\frac{4}{3}x\leq 0[/tex]
[tex]a=\frac{2}{3}\\b=\frac{4}{3}\\c=0\\delta=b^{2}-4ac=(\frac{4}{3})^{2}-4*\frac{2}{3}*0=(\frac{4}{3})^{2}=\frac{16}{9}\\\sqrt{delta}=\sqrt{\frac{16}{9}}=\frac{4}{3}[/tex]
[tex]x_{1}\frac{-b+\sqrt{delta}}{2a}=\frac{-\frac{4}{3}+\frac{4}{3}}{2*\frac{2}{3}}=\frac{0}{\frac{4}{3}}=0[/tex]
[tex]x_{2}=\frac{-b-\sqrt{delta}}{2a}=\frac{-\frac{4}{3}-\frac{4}{3}}{2*\frac{2}{3}}=\frac{-\frac{8}{3}}{\frac{4}{3}}=(-\frac{8}{3})*\frac{3}{4}=-2[/tex]
[tex]2.) -\frac{3}{5}x^{2}+\frac{9}{5}x\geq 0[/tex]
[tex]a=-\frac{3}{5}\\b=\frac{9}{5}\\c=0[/tex]
[tex]delta=b^{2}-4ac=(\frac{9}{5})^{2}-4*(-\frac{3}{5})*0=\frac{81}{25}[/tex]
[tex]\sqrt{delta}=\sqrt{\frac{81}{25}}=\frac{9}{5}[/tex]
[tex]x_{1}=\frac{-b+\sqrt{delta}}{2a}=\frac{-\frac{9}{5}+\frac{9}{5}}{2*(-\frac{3}{5})}=\frac{0}{-\frac{6}{5}}=0[/tex]
[tex]x_{2}=\frac{-b-\sqrt{delta}}{2a}=\frac{-\frac{9}{5}-\frac{9}{5}}{2*(-\frac{3}{5})}=\frac{-\frac{18}{5}}{-\frac{6}{5}}=(-\frac{18}{5}):(-\frac{6}{5})=(-\frac{18}{5})*(-\frac{5}{6})=3[/tex]
