11x2-108x-120=0

Solution for 11x2-108x-120=0 equation:

11x^2-108x-120=0

a = 11; b = -108; c = -120;
Δ = b2-4ac
Δ = -1082-4·11·(-120)
Δ = 16944
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:

$\sqrt{\Delta}=\sqrt{16944}=\sqrt{16*1059}=\sqrt{16}*\sqrt{1059}=4\sqrt{1059}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-4\sqrt{1059}}{2*11}=\frac{108-4\sqrt{1059}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+4\sqrt{1059}}{2*11}=\frac{108+4\sqrt{1059}}{22}
$