0=x^2+52x+192

Solution for 0=x^2+52x+192 equation:

0=x^2+52x+192

We move all terms to the left:

0-(x^2+52x+192)=0

We add all the numbers together, and all the variables

-(x^2+52x+192)=0

We get rid of parentheses

-x^2-52x-192=0

We add all the numbers together, and all the variables

-1x^2-52x-192=0

a = -1; b = -52; c = -192;
Δ = b2-4ac
Δ = -522-4·(-1)·(-192)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-44}{2*-1}=\frac{8}{-2}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+44}{2*-1}=\frac{96}{-2}
=-48
$