N=5,n2-2n+n

Solution for N=5,n2-2n+n equation:

=5.N^2-2N+N

We move all terms to the left:

-(5.N^2-2N+N)=0

We get rid of parentheses

-5.N^2+2N-N=0

We add all the numbers together, and all the variables

-5N^2+N=0

a = -5; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-5)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$N_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$N_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$N_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-5}=\frac{-2}{-10}
=1/5
$
$N_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-5}=\frac{0}{-10}
=0
$