0=19x+84+x^2

Solution for 0=19x+84+x^2 equation:

0=19x+84+x^2

We move all terms to the left:

0-(19x+84+x^2)=0

We add all the numbers together, and all the variables

-(19x+84+x^2)=0

We get rid of parentheses

-x^2-19x-84=0

We add all the numbers together, and all the variables

-1x^2-19x-84=0

a = -1; b = -19; c = -84;
Δ = b2-4ac
Δ = -192-4·(-1)·(-84)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-5}{2*-1}=\frac{14}{-2}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+5}{2*-1}=\frac{24}{-2}
=-12
$