11x^2-16x-91=0

Solution for 11x^2-16x-91=0 equation:

11x^2-16x-91=0

a = 11; b = -16; c = -91;
Δ = b2-4ac
Δ = -162-4·11·(-91)
Δ = 4260
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:

$\sqrt{\Delta}=\sqrt{4260}=\sqrt{4*1065}=\sqrt{4}*\sqrt{1065}=2\sqrt{1065}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{1065}}{2*11}=\frac{16-2\sqrt{1065}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{1065}}{2*11}=\frac{16+2\sqrt{1065}}{22}
$