5000=275n+25n^2-25n

Solution for 5000=275n+25n^2-25n equation:

5000=275n+25n^2-25n

We move all terms to the left:

5000-(275n+25n^2-25n)=0

We get rid of parentheses

-25n^2-275n+25n+5000=0

We add all the numbers together, and all the variables

-25n^2-250n+5000=0

a = -25; b = -250; c = +5000;
Δ = b2-4ac
Δ = -2502-4·(-25)·5000
Δ = 562500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{562500}=750$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-250)-750}{2*-25}=\frac{-500}{-50}
=+10
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-250)+750}{2*-25}=\frac{1000}{-50}
=-20
$