84=5x+x^2

Solution for 84=5x+x^2 equation:

84=5x+x^2

We move all terms to the left:

84-(5x+x^2)=0

We get rid of parentheses

-x^2-5x+84=0

We add all the numbers together, and all the variables

-1x^2-5x+84=0

a = -1; b = -5; c = +84;
Δ = b2-4ac
Δ = -52-4·(-1)·84
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-19}{2*-1}=\frac{-14}{-2}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+19}{2*-1}=\frac{24}{-2}
=-12
$