84=20x-x^2

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

84=20x-x^2

We move all terms to the left:

84-(20x-x^2)=0

We get rid of parentheses

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