2x^2-16x-113=0

Solution for 2x^2-16x-113=0 equation:

2x^2-16x-113=0

a = 2; b = -16; c = -113;
Δ = b2-4ac
Δ = -162-4·2·(-113)
Δ = 1160
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:

$\sqrt{\Delta}=\sqrt{1160}=\sqrt{4*290}=\sqrt{4}*\sqrt{290}=2\sqrt{290}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{290}}{2*2}=\frac{16-2\sqrt{290}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{290}}{2*2}=\frac{16+2\sqrt{290}}{4}
$