3n2-n=1000

Solution for 3n2-n=1000 equation:

3n^2-n=1000

We move all terms to the left:

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

We add all the numbers together, and all the variables

3n^2-1n-1000=0

a = 3; b = -1; c = -1000;
Δ = b2-4ac
Δ = -12-4·3·(-1000)
Δ = 12001
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{-(-1)-\sqrt{12001}}{2*3}=\frac{1-\sqrt{12001}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{12001}}{2*3}=\frac{1+\sqrt{12001}}{6}
$