400+4x^2-80x=64x^2

Solution for 400+4x^2-80x=64x^2 equation:

400+4x^2-80x=64x^2

We move all terms to the left:

400+4x^2-80x-(64x^2)=0

determiningTheFunctionDomain
4x^2-64x^2-80x+400=0

We add all the numbers together, and all the variables

-60x^2-80x+400=0

a = -60; b = -80; c = +400;
Δ = b2-4ac
Δ = -802-4·(-60)·400
Δ = 102400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{102400}=320$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-320}{2*-60}=\frac{-240}{-120}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+320}{2*-60}=\frac{400}{-120}
=-3+1/3
$