2n^2-12n-134=0

Solution for 2n^2-12n-134=0 equation:

2n^2-12n-134=0

a = 2; b = -12; c = -134;
Δ = b2-4ac
Δ = -122-4·2·(-134)
Δ = 1216
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:

$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{19}}{2*2}=\frac{12-8\sqrt{19}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{19}}{2*2}=\frac{12+8\sqrt{19}}{4}
$