-n^2+9=-8n

Solution for -n^2+9=-8n equation:

-n^2+9=-8n

We move all terms to the left:

-n^2+9-(-8n)=0

We add all the numbers together, and all the variables

-1n^2-(-8n)+9=0

We get rid of parentheses

-1n^2+8n+9=0

a = -1; b = 8; c = +9;
Δ = b2-4ac
Δ = 82-4·(-1)·9
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-10}{2*-1}=\frac{-18}{-2}
=+9
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+10}{2*-1}=\frac{2}{-2}
=-1
$