x^2-224*x-16*192=0

Solution for x^2-224*x-16*192=0 equation:

x^2-224x-16*192=0

We add all the numbers together, and all the variables

x^2-224x-3072=0

a = 1; b = -224; c = -3072;
Δ = b2-4ac
Δ = -2242-4·1·(-3072)
Δ = 62464
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:

$\sqrt{\Delta}=\sqrt{62464}=\sqrt{1024*61}=\sqrt{1024}*\sqrt{61}=32\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-224)-32\sqrt{61}}{2*1}=\frac{224-32\sqrt{61}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-224)+32\sqrt{61}}{2*1}=\frac{224+32\sqrt{61}}{2}
$