50n^2-80n=100n^2

Solution for 50n^2-80n=100n^2 equation:

50n^2-80n=100n^2

We move all terms to the left:

50n^2-80n-(100n^2)=0

determiningTheFunctionDomain
50n^2-100n^2-80n=0

We add all the numbers together, and all the variables

-50n^2-80n=0

a = -50; b = -80; c = 0;
Δ = b2-4ac
Δ = -802-4·(-50)·0
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-80}{2*-50}=\frac{0}{-100}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+80}{2*-50}=\frac{160}{-100}
=-1+3/5
$