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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3n^2-5n-8=0

a = 3; b = -5; c = -8;
Δ = b2-4ac
Δ = -52-4·3·(-8)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-11}{2*3}=\frac{-6}{6}
=-1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+11}{2*3}=\frac{16}{6}
=2+2/3
$