2+3(n-9)n=15

Solution for 2+3(n-9)n=15 equation:

2+3(n-9)n=15

We move all terms to the left:

2+3(n-9)n-(15)=0

We add all the numbers together, and all the variables

3(n-9)n-13=0

We multiply parentheses

3n^2-27n-13=0

a = 3; b = -27; c = -13;
Δ = b2-4ac
Δ = -272-4·3·(-13)
Δ = 885
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-\sqrt{885}}{2*3}=\frac{27-\sqrt{885}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{885}}{2*3}=\frac{27+\sqrt{885}}{6}
$