64x-12^2=x^2

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

64x-12^2=x^2

We move all terms to the left:

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

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

We add all the numbers together, and all the variables

-1x^2+64x-144=0

a = -1; b = 64; c = -144;
Δ = b2-4ac
Δ = 642-4·(-1)·(-144)
Δ = 3520
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:

$\sqrt{\Delta}=\sqrt{3520}=\sqrt{64*55}=\sqrt{64}*\sqrt{55}=8\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-8\sqrt{55}}{2*-1}=\frac{-64-8\sqrt{55}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+8\sqrt{55}}{2*-1}=\frac{-64+8\sqrt{55}}{-2}
$