2(4n+6)4n-2=2n+7n+6

Solution for 2(4n+6)4n-2=2n+7n+6 equation:

2(4n+6)4n-2=2n+7n+6

We move all terms to the left:

2(4n+6)4n-2-(2n+7n+6)=0

We add all the numbers together, and all the variables

2(4n+6)4n-(9n+6)-2=0

We multiply parentheses

32n^2+48n-(9n+6)-2=0

We get rid of parentheses

32n^2+48n-9n-6-2=0

We add all the numbers together, and all the variables

32n^2+39n-8=0

a = 32; b = 39; c = -8;
Δ = b2-4ac
Δ = 392-4·32·(-8)
Δ = 2545
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{-(39)-\sqrt{2545}}{2*32}=\frac{-39-\sqrt{2545}}{64}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+\sqrt{2545}}{2*32}=\frac{-39+\sqrt{2545}}{64}
$