17600=50n+20n^2/2

Solution for 17600=50n+20n^2/2 equation:

17600=50n+20n^2/2

We move all terms to the left:

17600-(50n+20n^2/2)=0

We get rid of parentheses

-20n^2/2-50n+17600=0

We multiply all the terms by the denominator


-20n^2-50n*2+17600*2=0

We add all the numbers together, and all the variables

-20n^2-50n*2+35200=0

Wy multiply elements

-20n^2-100n+35200=0

a = -20; b = -100; c = +35200;
Δ = b2-4ac
Δ = -1002-4·(-20)·35200
Δ = 2826000
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:

$\sqrt{\Delta}=\sqrt{2826000}=\sqrt{3600*785}=\sqrt{3600}*\sqrt{785}=60\sqrt{785}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-60\sqrt{785}}{2*-20}=\frac{100-60\sqrt{785}}{-40}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+60\sqrt{785}}{2*-20}=\frac{100+60\sqrt{785}}{-40}
$