[tex]-3x^2-4x+5=0\\\\a=-3;\ b=-4;\ c=5\\\Delta=b^2-4ac\\\\\Delta=(-4)^2-4\cdot(-3)\cdot5=16+60=76 \ \textgreater \ 0\\\\therefore\\\sqrt\Delta=\sqrt{76}=\sqrt{4\cdot19}=\sqrt4\cdot\sqrt{19}=2\sqrt{19}\\x_1=\dfrac{-b-\sqrt\Delta}{2a}\ and\ x_2=\dfrac{-b+\sqrt\Delta}{2a}\\\\x_1=\dfrac{4-2\sqrt{19}}{2\cdot(-3)}=\dfrac{4-2\sqrt{19}}{-6}=\boxed{-\dfrac{2-\sqrt{19}}{3}}\\\\x_2=\dfrac{4+2\sqrt{19}}{2\cdot(-3)}=\dfrac{4+2\sqrt{19}}{-6}=\boxed{-\dfrac{2+\sqrt{19}}{3}}[/tex]
