11x^2-32x-112=0

Solution for 11x^2-32x-112=0 equation:

11x^2-32x-112=0

a = 11; b = -32; c = -112;
Δ = b2-4ac
Δ = -322-4·11·(-112)
Δ = 5952
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:

$\sqrt{\Delta}=\sqrt{5952}=\sqrt{64*93}=\sqrt{64}*\sqrt{93}=8\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{93}}{2*11}=\frac{32-8\sqrt{93}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{93}}{2*11}=\frac{32+8\sqrt{93}}{22}
$