3n^2-2n-574=0

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

3n^2-2n-574=0

a = 3; b = -2; c = -574;
Δ = b2-4ac
Δ = -22-4·3·(-574)
Δ = 6892
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:

$\sqrt{\Delta}=\sqrt{6892}=\sqrt{4*1723}=\sqrt{4}*\sqrt{1723}=2\sqrt{1723}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{1723}}{2*3}=\frac{2-2\sqrt{1723}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{1723}}{2*3}=\frac{2+2\sqrt{1723}}{6}
$