In order to get the a,b,c values for the quadratic formula we need to put the equation in standered form:
[tex]ax^2+bx+c=0 [/tex]
We can do this by subtracting 1 from both sides:
[tex]11x^2-4x-1=1-1
[/tex]
Now we have:
[tex]11x^2-4x-1=0
[/tex]
a=11, b=-4, c=-1
Now you use the quadratic formula:
[tex] \frac{-b_-^+ \sqrt{b^2-4ac} }{2a} [/tex]
Now plug in the values of a,b,c
[tex] \frac{-(-4)_-^+ \sqrt{(-4)^2-4(11)(-1)} }{2(11)} [/tex]
Simplify it:
[tex]\frac{4_-^+ \sqrt{60} }{22} [/tex]
You can further simplify the given equation to get a final answer of:
[tex]x= \frac{2}{11}+ \frac{1}{11} \sqrt{15} [/tex]
or
[tex]x= \frac{2}{11}+ \frac{-1}{11} \sqrt{15} [/tex]
