0=-n+2n^2-250

Solution for 0=-n+2n^2-250 equation:

0=-n+2n^2-250

We move all terms to the left:

0-(-n+2n^2-250)=0

We add all the numbers together, and all the variables

-(-n+2n^2-250)=0

We get rid of parentheses

-2n^2+n+250=0

a = -2; b = 1; c = +250;
Δ = b2-4ac
Δ = 12-4·(-2)·250
Δ = 2001
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{2001}}{2*-2}=\frac{-1-\sqrt{2001}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{2001}}{2*-2}=\frac{-1+\sqrt{2001}}{-4}
$