64=6x^2

Solution for 64=6x^2 equation:

64=6x^2

We move all terms to the left:

64-(6x^2)=0

a = -6; b = 0; c = +64;
Δ = b2-4ac
Δ = 02-4·(-6)·64
Δ = 1536
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:

$\sqrt{\Delta}=\sqrt{1536}=\sqrt{256*6}=\sqrt{256}*\sqrt{6}=16\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{6}}{2*-6}=\frac{0-16\sqrt{6}}{-12}
=-\frac{16\sqrt{6}}{-12}
=-\frac{4\sqrt{6}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{6}}{2*-6}=\frac{0+16\sqrt{6}}{-12}
=\frac{16\sqrt{6}}{-12}
=\frac{4\sqrt{6}}{-3}
$