3n^2-3n-574=0

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

3n^2-3n-574=0

a = 3; b = -3; c = -574;
Δ = b2-4ac
Δ = -32-4·3·(-574)
Δ = 6897
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6897}=\sqrt{121*57}=\sqrt{121}*\sqrt{57}=11\sqrt{57}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-11\sqrt{57}}{2*3}=\frac{3-11\sqrt{57}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+11\sqrt{57}}{2*3}=\frac{3+11\sqrt{57}}{6}
$