256x2-676=4

Solution for 256x2-676=4 equation:

256x^2-676=4

We move all terms to the left:

256x^2-676-(4)=0

We add all the numbers together, and all the variables

256x^2-680=0

a = 256; b = 0; c = -680;
Δ = b2-4ac
Δ = 02-4·256·(-680)
Δ = 696320
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:

$\sqrt{\Delta}=\sqrt{696320}=\sqrt{4096*170}=\sqrt{4096}*\sqrt{170}=64\sqrt{170}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-64\sqrt{170}}{2*256}=\frac{0-64\sqrt{170}}{512}
=-\frac{64\sqrt{170}}{512}
=-\frac{\sqrt{170}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+64\sqrt{170}}{2*256}=\frac{0+64\sqrt{170}}{512}
=\frac{64\sqrt{170}}{512}
=\frac{\sqrt{170}}{8}
$