x2-2x-111=0

Solution for x2-2x-111=0 equation:

x2-2x-111=0

We add all the numbers together, and all the variables

x^2-2x-111=0

a = 1; b = -2; c = -111;
Δ = b2-4ac
Δ = -22-4·1·(-111)
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-8\sqrt{7}}{2*1}=\frac{2-8\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+8\sqrt{7}}{2*1}=\frac{2+8\sqrt{7}}{2}
$