11x2-2x-8=0

Solution for 11x2-2x-8=0 equation:

11x^2-2x-8=0

a = 11; b = -2; c = -8;
Δ = b2-4ac
Δ = -22-4·11·(-8)
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{89}}{2*11}=\frac{2-2\sqrt{89}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{89}}{2*11}=\frac{2+2\sqrt{89}}{22}
$