x2+768=64x

Solution for x2+768=64x equation:

x2+768=64x

We move all terms to the left:

x2+768-(64x)=0

We add all the numbers together, and all the variables

x^2-64x+768=0

a = 1; b = -64; c = +768;
Δ = b2-4ac
Δ = -642-4·1·768
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-32}{2*1}=\frac{32}{2}
=16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+32}{2*1}=\frac{96}{2}
=48
$