19x-x2-84=0

Solution for 19x-x2-84=0 equation:

19x-x2-84=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{-24}{-2}
=+12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+5}{2*-1}=\frac{-14}{-2}
=+7
$