64x-12x^2=x^2

Solution for 64x-12x^2=x^2 equation:

64x-12x^2=x^2

We move all terms to the left:

64x-12x^2-(x^2)=0

determiningTheFunctionDomain
-12x^2-x^2+64x=0

We add all the numbers together, and all the variables

-13x^2+64x=0

a = -13; b = 64; c = 0;
Δ = b2-4ac
Δ = 642-4·(-13)·0
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-64}{2*-13}=\frac{-128}{-26}
=4+12/13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+64}{2*-13}=\frac{0}{-26}
=0
$