6^4-6x^2+8=0

Solution for 6^4-6x^2+8=0 equation:

6^4-6x^2+8=0

We add all the numbers together, and all the variables

-6x^2+1304=0

a = -6; b = 0; c = +1304;
Δ = b2-4ac
Δ = 02-4·(-6)·1304
Δ = 31296
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:

$\sqrt{\Delta}=\sqrt{31296}=\sqrt{64*489}=\sqrt{64}*\sqrt{489}=8\sqrt{489}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{489}}{2*-6}=\frac{0-8\sqrt{489}}{-12}
=-\frac{8\sqrt{489}}{-12}
=-\frac{2\sqrt{489}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{489}}{2*-6}=\frac{0+8\sqrt{489}}{-12}
=\frac{8\sqrt{489}}{-12}
=\frac{2\sqrt{489}}{-3}
$