3n+10=n^2+8n+16

Solution for 3n+10=n^2+8n+16 equation:

3n+10=n^2+8n+16

We move all terms to the left:

3n+10-(n^2+8n+16)=0

We get rid of parentheses

-n^2+3n-8n-16+10=0

We add all the numbers together, and all the variables

-1n^2-5n-6=0

a = -1; b = -5; c = -6;
Δ = b2-4ac
Δ = -52-4·(-1)·(-6)
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{-(-5)-1}{2*-1}=\frac{4}{-2}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+1}{2*-1}=\frac{6}{-2}
=-3
$