3n^2-2n=645

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

3n^2-2n=645

We move all terms to the left:

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