n^2-9n+8=-6

Solution for n^2-9n+8=-6 equation:

n^2-9n+8=-6

We move all terms to the left:

n^2-9n+8-(-6)=0

We add all the numbers together, and all the variables

n^2-9n+14=0

a = 1; b = -9; c = +14;
Δ = b2-4ac
Δ = -92-4·1·14
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-5}{2*1}=\frac{4}{2}
=2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+5}{2*1}=\frac{14}{2}
=7
$