5n^2-2n-997=0

Solution for 5n^2-2n-997=0 equation:

5n^2-2n-997=0

a = 5; b = -2; c = -997;
Δ = b2-4ac
Δ = -22-4·5·(-997)
Δ = 19944
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:

$\sqrt{\Delta}=\sqrt{19944}=\sqrt{36*554}=\sqrt{36}*\sqrt{554}=6\sqrt{554}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6\sqrt{554}}{2*5}=\frac{2-6\sqrt{554}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6\sqrt{554}}{2*5}=\frac{2+6\sqrt{554}}{10}
$