0=3n^2-n-574

Solution for 0=3n^2-n-574 equation:

0=3n^2-n-574

We move all terms to the left:

0-(3n^2-n-574)=0

We add all the numbers together, and all the variables

-(3n^2-n-574)=0

We get rid of parentheses

-3n^2+n+574=0

a = -3; b = 1; c = +574;
Δ = b2-4ac
Δ = 12-4·(-3)·574
Δ = 6889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6889}=83$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-83}{2*-3}=\frac{-84}{-6}
=+14
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+83}{2*-3}=\frac{82}{-6}
=-13+2/3
$