6n(n-1)+4n=3

Solution for 6n(n-1)+4n=3 equation:

6n(n-1)+4n=3

We move all terms to the left:

6n(n-1)+4n-(3)=0

We add all the numbers together, and all the variables

4n+6n(n-1)-3=0

We multiply parentheses

6n^2+4n-6n-3=0

We add all the numbers together, and all the variables

6n^2-2n-3=0

a = 6; b = -2; c = -3;
Δ = b2-4ac
Δ = -22-4·6·(-3)
Δ = 76
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{19}}{2*6}=\frac{2-2\sqrt{19}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{19}}{2*6}=\frac{2+2\sqrt{19}}{12}
$