12n^2-24n=96

Solution for 12n^2-24n=96 equation:

12n^2-24n=96

We move all terms to the left:

12n^2-24n-(96)=0

a = 12; b = -24; c = -96;
Δ = b2-4ac
Δ = -242-4·12·(-96)
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-72}{2*12}=\frac{-48}{24}
=-2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+72}{2*12}=\frac{96}{24}
=4
$