11x^2-4x-2=0

Solution for 11x^2-4x-2=0 equation:

11x^2-4x-2=0

a = 11; b = -4; c = -2;
Δ = b2-4ac
Δ = -42-4·11·(-2)
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{26}}{2*11}=\frac{4-2\sqrt{26}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{26}}{2*11}=\frac{4+2\sqrt{26}}{22}
$