3n^2-2n+1=-3n^2+9n+1

Solution for 3n^2-2n+1=-3n^2+9n+1 equation:

3n^2-2n+1=-3n^2+9n+1

We move all terms to the left:

3n^2-2n+1-(-3n^2+9n+1)=0

We get rid of parentheses

3n^2+3n^2-9n-2n-1+1=0

We add all the numbers together, and all the variables

6n^2-11n=0

a = 6; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·6·0
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{-(-11)-11}{2*6}=\frac{0}{12}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*6}=\frac{22}{12}
=1+5/6
$