11x^2-8x-4=0

Solution for 11x^2-8x-4=0 equation:

11x^2-8x-4=0

a = 11; b = -8; c = -4;
Δ = b2-4ac
Δ = -82-4·11·(-4)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{15}}{2*11}=\frac{8-4\sqrt{15}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{15}}{2*11}=\frac{8+4\sqrt{15}}{22}
$