X2-4y2+64=0

Solution for X2-4y2+64=0 equation:

X2-4X^2+64=0

We add all the numbers together, and all the variables

-3X^2+64=0

a = -3; b = 0; c = +64;
Δ = b2-4ac
Δ = 02-4·(-3)·64
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{3}}{2*-3}=\frac{0-16\sqrt{3}}{-6}
=-\frac{16\sqrt{3}}{-6}
=-\frac{8\sqrt{3}}{-3}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{3}}{2*-3}=\frac{0+16\sqrt{3}}{-6}
=\frac{16\sqrt{3}}{-6}
=\frac{8\sqrt{3}}{-3}
$