3n^2-2n=21

Solution for 3n^2-2n=21 equation:

3n^2-2n=21

We move all terms to the left:

3n^2-2n-(21)=0

a = 3; b = -2; c = -21;
Δ = b2-4ac
Δ = -22-4·3·(-21)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-16}{2*3}=\frac{-14}{6}
=-2+1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+16}{2*3}=\frac{18}{6}
=3
$