3n^2-3n+2=1000

Solution for 3n^2-3n+2=1000 equation:

3n^2-3n+2=1000

We move all terms to the left:

3n^2-3n+2-(1000)=0

We add all the numbers together, and all the variables

3n^2-3n-998=0

a = 3; b = -3; c = -998;
Δ = b2-4ac
Δ = -32-4·3·(-998)
Δ = 11985
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{11985}}{2*3}=\frac{3-\sqrt{11985}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{11985}}{2*3}=\frac{3+\sqrt{11985}}{6}
$