3(7n+13)12n+15=2

Solution for 3(7n+13)12n+15=2 equation:

3(7n+13)12n+15=2

We move all terms to the left:

3(7n+13)12n+15-(2)=0

We add all the numbers together, and all the variables

3(7n+13)12n+13=0

We multiply parentheses

252n^2+468n+13=0

a = 252; b = 468; c = +13;
Δ = b2-4ac
Δ = 4682-4·252·13
Δ = 205920
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:

$\sqrt{\Delta}=\sqrt{205920}=\sqrt{144*1430}=\sqrt{144}*\sqrt{1430}=12\sqrt{1430}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(468)-12\sqrt{1430}}{2*252}=\frac{-468-12\sqrt{1430}}{504}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(468)+12\sqrt{1430}}{2*252}=\frac{-468+12\sqrt{1430}}{504}
$