4n^2-2n=12

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

4n^2-2n=12

We move all terms to the left:

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

a = 4; b = -2; c = -12;
Δ = b2-4ac
Δ = -22-4·4·(-12)
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*4}=\frac{-12}{8}
=-1+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+14}{2*4}=\frac{16}{8}
=2
$