n^2-14n+11=6-8n

Solution for n^2-14n+11=6-8n equation:

n^2-14n+11=6-8n

We move all terms to the left:

n^2-14n+11-(6-8n)=0

We add all the numbers together, and all the variables

n^2-14n-(-8n+6)+11=0

We get rid of parentheses

n^2-14n+8n-6+11=0

We add all the numbers together, and all the variables

n^2-6n+5=0

a = 1; b = -6; c = +5;
Δ = b2-4ac
Δ = -62-4·1·5
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4}{2*1}=\frac{2}{2}
=1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4}{2*1}=\frac{10}{2}
=5
$