11x^2-20x-1=0

Solution for 11x^2-20x-1=0 equation:

11x^2-20x-1=0

a = 11; b = -20; c = -1;
Δ = b2-4ac
Δ = -202-4·11·(-1)
Δ = 444
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:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{111}}{2*11}=\frac{20-2\sqrt{111}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{111}}{2*11}=\frac{20+2\sqrt{111}}{22}
$