2x^2-2x-113=0

Solution for 2x^2-2x-113=0 equation:

2x^2-2x-113=0

a = 2; b = -2; c = -113;
Δ = b2-4ac
Δ = -22-4·2·(-113)
Δ = 908
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:

$\sqrt{\Delta}=\sqrt{908}=\sqrt{4*227}=\sqrt{4}*\sqrt{227}=2\sqrt{227}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{227}}{2*2}=\frac{2-2\sqrt{227}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{227}}{2*2}=\frac{2+2\sqrt{227}}{4}
$