6x^2-48x-192=0

Solution for 6x^2-48x-192=0 equation:

6x^2-48x-192=0

a = 6; b = -48; c = -192;
Δ = b2-4ac
Δ = -482-4·6·(-192)
Δ = 6912
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6912}=\sqrt{2304*3}=\sqrt{2304}*\sqrt{3}=48\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-48\sqrt{3}}{2*6}=\frac{48-48\sqrt{3}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+48\sqrt{3}}{2*6}=\frac{48+48\sqrt{3}}{12}
$