12n^2+48n-1152=0

Solution for 12n^2+48n-1152=0 equation:

12n^2+48n-1152=0

a = 12; b = 48; c = -1152;
Δ = b2-4ac
Δ = 482-4·12·(-1152)
Δ = 57600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{57600}=240$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-240}{2*12}=\frac{-288}{24}
=-12
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+240}{2*12}=\frac{192}{24}
=8
$