4n(n+3)=6n+8+2n

Solution for 4n(n+3)=6n+8+2n equation:

4n(n+3)=6n+8+2n

We move all terms to the left:

4n(n+3)-(6n+8+2n)=0

We add all the numbers together, and all the variables

4n(n+3)-(8n+8)=0

We multiply parentheses

4n^2+12n-(8n+8)=0

We get rid of parentheses

4n^2+12n-8n-8=0

We add all the numbers together, and all the variables

4n^2+4n-8=0

a = 4; b = 4; c = -8;
Δ = b2-4ac
Δ = 42-4·4·(-8)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-12}{2*4}=\frac{-16}{8}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+12}{2*4}=\frac{8}{8}
=1
$