2n^2-6n-13=0

Solution for 2n^2-6n-13=0 equation:

2n^2-6n-13=0

a = 2; b = -6; c = -13;
Δ = b2-4ac
Δ = -62-4·2·(-13)
Δ = 140
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:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{35}}{2*2}=\frac{6-2\sqrt{35}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{35}}{2*2}=\frac{6+2\sqrt{35}}{4}
$