12x^2-144x+384=0.

Solution for 12x^2-144x+384=0. equation:

12x^2-144x+384=0.

a = 12; b = -144; c = +384;
Δ = b2-4ac
Δ = -1442-4·12·384
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-48}{2*12}=\frac{96}{24}
=4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+48}{2*12}=\frac{192}{24}
=8
$