6(n^2+7n+6)=n^2-1

Solution for 6(n^2+7n+6)=n^2-1 equation:

6(n^2+7n+6)=n^2-1

We move all terms to the left:

6(n^2+7n+6)-(n^2-1)=0

We multiply parentheses

6n^2+42n-(n^2-1)+36=0

We get rid of parentheses

6n^2-n^2+42n+1+36=0

We add all the numbers together, and all the variables

5n^2+42n+37=0

a = 5; b = 42; c = +37;
Δ = b2-4ac
Δ = 422-4·5·37
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-32}{2*5}=\frac{-74}{10}
=-7+2/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+32}{2*5}=\frac{-10}{10}
=-1
$