n2+n-2011=0

Solution for n2+n-2011=0 equation:

n2+n-2011=0

We add all the numbers together, and all the variables

n^2+n-2011=0

a = 1; b = 1; c = -2011;
Δ = b2-4ac
Δ = 12-4·1·(-2011)
Δ = 8045
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{8045}}{2*1}=\frac{-1-\sqrt{8045}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{8045}}{2*1}=\frac{-1+\sqrt{8045}}{2}
$