we have the equation
2x^2-11x=1
2x^2-11x-1=0
where
a=2
b=-11
c=-1
substitute in the quadratic formula
[tex]x=\frac{-(-11)\pm\sqrt[]{(-11)^2-4(2)(-1)}}{2(2)}[/tex][tex]x=\frac{11\pm\sqrt[]{129}}{4}[/tex]the solutions are
[tex]x=\frac{11+\sqrt[]{129}}{4}\text{ and }x=\frac{11-\sqrt[]{129}}{4}[/tex]