0=x^2+19x-204

Solution for 0=x^2+19x-204 equation:

0=x^2+19x-204

We move all terms to the left:

0-(x^2+19x-204)=0

We add all the numbers together, and all the variables

-(x^2+19x-204)=0

We get rid of parentheses

-x^2-19x+204=0

We add all the numbers together, and all the variables

-1x^2-19x+204=0

a = -1; b = -19; c = +204;
Δ = b2-4ac
Δ = -192-4·(-1)·204
Δ = 1177
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{1177}}{2*-1}=\frac{19-\sqrt{1177}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{1177}}{2*-1}=\frac{19+\sqrt{1177}}{-2}
$