n^2-9-2n+6=9-n

Solution for n^2-9-2n+6=9-n equation:

n^2-9-2n+6=9-n

We move all terms to the left:

n^2-9-2n+6-(9-n)=0

We add all the numbers together, and all the variables

n^2-2n-(-1n+9)-9+6=0

We add all the numbers together, and all the variables

n^2-2n-(-1n+9)-3=0

We get rid of parentheses

n^2-2n+1n-9-3=0

We add all the numbers together, and all the variables

n^2-1n-12=0

a = 1; b = -1; c = -12;
Δ = b2-4ac
Δ = -12-4·1·(-12)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-7}{2*1}=\frac{-6}{2}
=-3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+7}{2*1}=\frac{8}{2}
=4
$