[tex]2x^2-2x-9=0\\\\Use\ the\ quadratic\ formula\\\\ax^2+bx+c=0\\\\\Delta=b^2-4ac\\\\if\ \Delta > 0\ then\ solutions\ are\ equal\\\\x_1=\dfrac{-b-\sqrt\Delta}{2a}\ and\ x_2=\dfrac{-b+\sqrt\Delta}{2a}[/tex]
[tex]a=2;\ b=-2;\ c=-9\\\\\Delta=(-2)^2-4\cdot2\cdpt(-9)=4+72=76 > 0\\\\\sqrt\Delta=\sqrt{76}=\sqrt{4\cdot19}=2\sqrt{19}\\\\x_1=\dfrac{-(-2)-2\sqrt{19}}{2\cdot2}=\dfrac{2-2\sqrt{19}}{4}=\dfrac{1-\sqrt{19}}{2}\\\\x_2=\dfrac{-(-2)+2\sqrt{19}}{2\cdot2}=\dfrac{2+2\sqrt{19}}{4}=\dfrac{1+\sqrt{19}}{2}[/tex]
