[tex]\displaystyle 1-3x(x-1)=-8 \\ 1-3x^2+3x=-8 \\ -3x^2+3x=-8-1 \\ -3x^2+3x=-9 \\ -3x^2+3x+9=0 \\ a=-3,b=3,c=9 \\ \Delta=b^2-4ac=3^2-4 \cdot (-3) \cdot 9=9+108=117 \\ x_1= \frac{-3+ \sqrt{117} }{2 \cdot (-3)} = \frac{-3+3 \sqrt{13} }{-6} = \frac{-3(1- \sqrt{13} )}{-6} = \frac{1- \sqrt{13} }{2} \\ \\ x_2= \frac{-3- \sqrt{117} }{2 \cdot (-3)} = \frac{-3-3 \sqrt{13} }{-6} = \frac{-3(1+ \sqrt{13} )}{-6} = \frac{1+ \sqrt{13} }{2} [/tex]
