6n(n+3)=24+3

Solution for 6n(n+3)=24+3 equation:

6n(n+3)=24+3

We move all terms to the left:

6n(n+3)-(24+3)=0

We add all the numbers together, and all the variables

6n(n+3)-27=0

We multiply parentheses

6n^2+18n-27=0

a = 6; b = 18; c = -27;
Δ = b2-4ac
Δ = 182-4·6·(-27)
Δ = 972
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:

$\sqrt{\Delta}=\sqrt{972}=\sqrt{324*3}=\sqrt{324}*\sqrt{3}=18\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18\sqrt{3}}{2*6}=\frac{-18-18\sqrt{3}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18\sqrt{3}}{2*6}=\frac{-18+18\sqrt{3}}{12}
$