6n^2+24n-72=0

Solution for 6n^2+24n-72=0 equation:

6n^2+24n-72=0

a = 6; b = 24; c = -72;
Δ = b2-4ac
Δ = 242-4·6·(-72)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-48}{2*6}=\frac{-72}{12}
=-6
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+48}{2*6}=\frac{24}{12}
=2
$