x^2-48x+576=16x

Solution for x^2-48x+576=16x equation:

x^2-48x+576=16x

We move all terms to the left:

x^2-48x+576-(16x)=0

We add all the numbers together, and all the variables

x^2-64x+576=0

a = 1; b = -64; c = +576;
Δ = b2-4ac
Δ = -642-4·1·576
Δ = 1792
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1792}=\sqrt{256*7}=\sqrt{256}*\sqrt{7}=16\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-16\sqrt{7}}{2*1}=\frac{64-16\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+16\sqrt{7}}{2*1}=\frac{64+16\sqrt{7}}{2}
$