2n2+12n=24

Solution for 2n2+12n=24 equation:

2n^2+12n=24

We move all terms to the left:

2n^2+12n-(24)=0

a = 2; b = 12; c = -24;
Δ = b2-4ac
Δ = 122-4·2·(-24)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{21}}{2*2}=\frac{-12-4\sqrt{21}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{21}}{2*2}=\frac{-12+4\sqrt{21}}{4}
$