4x^2-4x-111=0

Solution for 4x^2-4x-111=0 equation:

4x^2-4x-111=0

a = 4; b = -4; c = -111;
Δ = b2-4ac
Δ = -42-4·4·(-111)
Δ = 1792
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:

$\sqrt{\Delta}=\sqrt{1792}=\sqrt{256*7}=\sqrt{256}*\sqrt{7}=16\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-16\sqrt{7}}{2*4}=\frac{4-16\sqrt{7}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+16\sqrt{7}}{2*4}=\frac{4+16\sqrt{7}}{8}
$