3n(n+5)=3n+8

Solution for 3n(n+5)=3n+8 equation:

3n(n+5)=3n+8

We move all terms to the left:

3n(n+5)-(3n+8)=0

We multiply parentheses

3n^2+15n-(3n+8)=0

We get rid of parentheses

3n^2+15n-3n-8=0

We add all the numbers together, and all the variables

3n^2+12n-8=0

a = 3; b = 12; c = -8;
Δ = b2-4ac
Δ = 122-4·3·(-8)
Δ = 240
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{15}}{2*3}=\frac{-12-4\sqrt{15}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{15}}{2*3}=\frac{-12+4\sqrt{15}}{6}
$