-x^2+20x-84=0

Solution for -x^2+20x-84=0 equation:

-x^2+20x-84=0

We add all the numbers together, and all the variables

-1x^2+20x-84=0

a = -1; b = 20; c = -84;
Δ = b2-4ac
Δ = 202-4·(-1)·(-84)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-8}{2*-1}=\frac{-28}{-2}
=+14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+8}{2*-1}=\frac{-12}{-2}
=+6
$