3n^2+2n-456=0

Solution for 3n^2+2n-456=0 equation:

3n^2+2n-456=0

a = 3; b = 2; c = -456;
Δ = b2-4ac
Δ = 22-4·3·(-456)
Δ = 5476
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5476}=74$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-74}{2*3}=\frac{-76}{6}
=-12+2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+74}{2*3}=\frac{72}{6}
=12
$