-3n^2-4n+84=0

Solution for -3n^2-4n+84=0 equation:

-3n^2-4n+84=0

a = -3; b = -4; c = +84;
Δ = b2-4ac
Δ = -42-4·(-3)·84
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-32}{2*-3}=\frac{-28}{-6}
=4+2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+32}{2*-3}=\frac{36}{-6}
=-6
$