11x^2-121x-308=0

Solution for 11x^2-121x-308=0 equation:

11x^2-121x-308=0

a = 11; b = -121; c = -308;
Δ = b2-4ac
Δ = -1212-4·11·(-308)
Δ = 28193
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:

$\sqrt{\Delta}=\sqrt{28193}=\sqrt{121*233}=\sqrt{121}*\sqrt{233}=11\sqrt{233}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-121)-11\sqrt{233}}{2*11}=\frac{121-11\sqrt{233}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-121)+11\sqrt{233}}{2*11}=\frac{121+11\sqrt{233}}{22}
$