4(n+6)=4n+8)n+13

Solution for 4(n+6)=4n+8)n+13 equation:

4(n+6)=4n+8)n+13

We move all terms to the left:

4(n+6)-(4n+8)n+13)=0

We add all the numbers together, and all the variables

4(n+6)-(4n+8)n=0

We multiply parentheses

-4n^2+4n-8n+24=0

We add all the numbers together, and all the variables

-4n^2-4n+24=0

a = -4; b = -4; c = +24;
Δ = b2-4ac
Δ = -42-4·(-4)·24
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-20}{2*-4}=\frac{-16}{-8}
=+2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+20}{2*-4}=\frac{24}{-8}
=-3
$