645=3n^2-2n

Solution for 645=3n^2-2n equation:

645=3n^2-2n

We move all terms to the left:

645-(3n^2-2n)=0

We get rid of parentheses

-3n^2+2n+645=0

a = -3; b = 2; c = +645;
Δ = b2-4ac
Δ = 22-4·(-3)·645
Δ = 7744
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7744}=88$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-88}{2*-3}=\frac{-90}{-6}
=+15
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+88}{2*-3}=\frac{86}{-6}
=-14+1/3
$