13n^2-16n-17=0

Solution for 13n^2-16n-17=0 equation:

13n^2-16n-17=0

a = 13; b = -16; c = -17;
Δ = b2-4ac
Δ = -162-4·13·(-17)
Δ = 1140
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:

$\sqrt{\Delta}=\sqrt{1140}=\sqrt{4*285}=\sqrt{4}*\sqrt{285}=2\sqrt{285}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{285}}{2*13}=\frac{16-2\sqrt{285}}{26}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{285}}{2*13}=\frac{16+2\sqrt{285}}{26}
$