x^2-48x-192=0

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

x^2-48x-192=0

a = 1; b = -48; c = -192;
Δ = b2-4ac
Δ = -482-4·1·(-192)
Δ = 3072
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:

$\sqrt{\Delta}=\sqrt{3072}=\sqrt{1024*3}=\sqrt{1024}*\sqrt{3}=32\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-32\sqrt{3}}{2*1}=\frac{48-32\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+32\sqrt{3}}{2*1}=\frac{48+32\sqrt{3}}{2}
$