11x2-4x-1=0

Solution for 11x2-4x-1=0 equation:

11x^2-4x-1=0

a = 11; b = -4; c = -1;
Δ = b2-4ac
Δ = -42-4·11·(-1)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{15}}{2*11}=\frac{4-2\sqrt{15}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{15}}{2*11}=\frac{4+2\sqrt{15}}{22}
$