(X2-2)2+(x2-4)2=4

Solution for (X2-2)2+(x2-4)2=4 equation:

(X2-2)2+(X2-4)2=4

We move all terms to the left:

(X2-2)2+(X2-4)2-(4)=0

We add all the numbers together, and all the variables

(+X^2-2)2+(+X^2-4)2-4=0

We multiply parentheses

2X^2+2X^2-4-8-4=0

We add all the numbers together, and all the variables

4X^2-16=0

a = 4; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·4·(-16)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16}{2*4}=\frac{-16}{8}
=-2
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16}{2*4}=\frac{16}{8}
=2
$