-3n^2+2n+33=0

Solution for -3n^2+2n+33=0 equation:

-3n^2+2n+33=0

a = -3; b = 2; c = +33;
Δ = b2-4ac
Δ = 22-4·(-3)·33
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-20}{2*-3}=\frac{-22}{-6}
=3+2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+20}{2*-3}=\frac{18}{-6}
=-3
$