5n^2+n-400=0

Solution for 5n^2+n-400=0 equation:

5n^2+n-400=0

a = 5; b = 1; c = -400;
Δ = b2-4ac
Δ = 12-4·5·(-400)
Δ = 8001
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:

$\sqrt{\Delta}=\sqrt{8001}=\sqrt{9*889}=\sqrt{9}*\sqrt{889}=3\sqrt{889}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{889}}{2*5}=\frac{-1-3\sqrt{889}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{889}}{2*5}=\frac{-1+3\sqrt{889}}{10}
$