6n^2+18n-108=6n+5n^2

Solution for 6n^2+18n-108=6n+5n^2 equation:

6n^2+18n-108=6n+5n^2

We move all terms to the left:

6n^2+18n-108-(6n+5n^2)=0

We get rid of parentheses

6n^2-5n^2-6n+18n-108=0

We add all the numbers together, and all the variables

n^2+12n-108=0

a = 1; b = 12; c = -108;
Δ = b2-4ac
Δ = 122-4·1·(-108)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-24}{2*1}=\frac{-36}{2}
=-18
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+24}{2*1}=\frac{12}{2}
=6
$