20x=x^2+64

Solution for 20x=x^2+64 equation:

20x=x^2+64

We move all terms to the left:

20x-(x^2+64)=0

We get rid of parentheses

-x^2+20x-64=0

We add all the numbers together, and all the variables

-1x^2+20x-64=0

a = -1; b = 20; c = -64;
Δ = b2-4ac
Δ = 202-4·(-1)·(-64)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-12}{2*-1}=\frac{-32}{-2}
=+16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+12}{2*-1}=\frac{-8}{-2}
=+4
$