13n^2-n-34=0

Solution for 13n^2-n-34=0 equation:

13n^2-n-34=0

We add all the numbers together, and all the variables

13n^2-1n-34=0

a = 13; b = -1; c = -34;
Δ = b2-4ac
Δ = -12-4·13·(-34)
Δ = 1769
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{1769}}{2*13}=\frac{1-\sqrt{1769}}{26}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1769}}{2*13}=\frac{1+\sqrt{1769}}{26}
$