x^2=64-80x+16x^2

Solution for x^2=64-80x+16x^2 equation:

x^2=64-80x+16x^2

We move all terms to the left:

x^2-(64-80x+16x^2)=0

We get rid of parentheses

x^2-16x^2+80x-64=0

We add all the numbers together, and all the variables

-15x^2+80x-64=0

a = -15; b = 80; c = -64;
Δ = b2-4ac
Δ = 802-4·(-15)·(-64)
Δ = 2560
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:

$\sqrt{\Delta}=\sqrt{2560}=\sqrt{256*10}=\sqrt{256}*\sqrt{10}=16\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-16\sqrt{10}}{2*-15}=\frac{-80-16\sqrt{10}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+16\sqrt{10}}{2*-15}=\frac{-80+16\sqrt{10}}{-30}
$