(x2-8)2+x2-8=20

Solution for (x2-8)2+x2-8=20 equation:

(x2-8)2+x2-8=20

We move all terms to the left:

(x2-8)2+x2-8-(20)=0

We add all the numbers together, and all the variables

(+x^2-8)2+x2-8-20=0

We add all the numbers together, and all the variables

x^2+(+x^2-8)2-28=0

We multiply parentheses

x^2+2x^2-16-28=0

We add all the numbers together, and all the variables

3x^2-44=0

a = 3; b = 0; c = -44;
Δ = b2-4ac
Δ = 02-4·3·(-44)
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{33}}{2*3}=\frac{0-4\sqrt{33}}{6}
=-\frac{4\sqrt{33}}{6}
=-\frac{2\sqrt{33}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{33}}{2*3}=\frac{0+4\sqrt{33}}{6}
=\frac{4\sqrt{33}}{6}
=\frac{2\sqrt{33}}{3}
$