4=12n^2+2n

Solution for 4=12n^2+2n equation:

4=12n^2+2n

We move all terms to the left:

4-(12n^2+2n)=0

We get rid of parentheses

-12n^2-2n+4=0

a = -12; b = -2; c = +4;
Δ = b2-4ac
Δ = -22-4·(-12)·4
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-14}{2*-12}=\frac{-12}{-24}
=1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+14}{2*-12}=\frac{16}{-24}
=-2/3
$