3(2n-1)n=3

Solution for 3(2n-1)n=3 equation:

3(2n-1)n=3

We move all terms to the left:

3(2n-1)n-(3)=0

We multiply parentheses

6n^2-3n-3=0

a = 6; b = -3; c = -3;
Δ = b2-4ac
Δ = -32-4·6·(-3)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-9}{2*6}=\frac{-6}{12}
=-1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+9}{2*6}=\frac{12}{12}
=1
$