-2n-5n^2=n-4n^2

Solution for -2n-5n^2=n-4n^2 equation:

-2n-5n^2=n-4n^2

We move all terms to the left:

-2n-5n^2-(n-4n^2)=0

We get rid of parentheses

-5n^2+4n^2-n-2n=0

We add all the numbers together, and all the variables

-1n^2-3n=0

a = -1; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-1)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-1}=\frac{0}{-2}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-1}=\frac{6}{-2}
=-3
$