6n^2+12n-72=0

Solution for 6n^2+12n-72=0 equation:

6n^2+12n-72=0

a = 6; b = 12; c = -72;
Δ = b2-4ac
Δ = 122-4·6·(-72)
Δ = 1872
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:

$\sqrt{\Delta}=\sqrt{1872}=\sqrt{144*13}=\sqrt{144}*\sqrt{13}=12\sqrt{13}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{13}}{2*6}=\frac{-12-12\sqrt{13}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{13}}{2*6}=\frac{-12+12\sqrt{13}}{12}
$