3n^2+9n-2n-6=2n^2+8

Solution for 3n^2+9n-2n-6=2n^2+8 equation:

3n^2+9n-2n-6=2n^2+8

We move all terms to the left:

3n^2+9n-2n-6-(2n^2+8)=0

We add all the numbers together, and all the variables

3n^2+7n-(2n^2+8)-6=0

We get rid of parentheses

3n^2-2n^2+7n-8-6=0

We add all the numbers together, and all the variables

n^2+7n-14=0

a = 1; b = 7; c = -14;
Δ = b2-4ac
Δ = 72-4·1·(-14)
Δ = 105
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{-(7)-\sqrt{105}}{2*1}=\frac{-7-\sqrt{105}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{105}}{2*1}=\frac{-7+\sqrt{105}}{2}
$