2n^2-2n-127=0

Solution for 2n^2-2n-127=0 equation:

2n^2-2n-127=0

a = 2; b = -2; c = -127;
Δ = b2-4ac
Δ = -22-4·2·(-127)
Δ = 1020
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1020}=\sqrt{4*255}=\sqrt{4}*\sqrt{255}=2\sqrt{255}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{255}}{2*2}=\frac{2-2\sqrt{255}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{255}}{2*2}=\frac{2+2\sqrt{255}}{4}
$