6x^2=256

Solution for 6x^2=256 equation:

6x^2=256

We move all terms to the left:

6x^2-(256)=0

a = 6; b = 0; c = -256;
Δ = b2-4ac
Δ = 02-4·6·(-256)
Δ = 6144
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:

$\sqrt{\Delta}=\sqrt{6144}=\sqrt{1024*6}=\sqrt{1024}*\sqrt{6}=32\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{6}}{2*6}=\frac{0-32\sqrt{6}}{12}
=-\frac{32\sqrt{6}}{12}
=-\frac{8\sqrt{6}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{6}}{2*6}=\frac{0+32\sqrt{6}}{12}
=\frac{32\sqrt{6}}{12}
=\frac{8\sqrt{6}}{3}
$