0=x^2-11X-1

Solution for 0=x^2-11X-1 equation:

0=x^2-11x-1

We move all terms to the left:

0-(x^2-11x-1)=0

We add all the numbers together, and all the variables

-(x^2-11x-1)=0

We get rid of parentheses

-x^2+11x+1=0

We add all the numbers together, and all the variables

-1x^2+11x+1=0

a = -1; b = 11; c = +1;
Δ = b2-4ac
Δ = 112-4·(-1)·1
Δ = 125
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{125}=\sqrt{25*5}=\sqrt{25}*\sqrt{5}=5\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-5\sqrt{5}}{2*-1}=\frac{-11-5\sqrt{5}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+5\sqrt{5}}{2*-1}=\frac{-11+5\sqrt{5}}{-2}
$