(X2-3)2+(x2+1)2=26

Solution for (X2-3)2+(x2+1)2=26 equation:

(X2-3)2+(X2+1)2=26

We move all terms to the left:

(X2-3)2+(X2+1)2-(26)=0

We add all the numbers together, and all the variables

(+X^2-3)2+(+X^2+1)2-26=0

We multiply parentheses

2X^2+2X^2-6+2-26=0

We add all the numbers together, and all the variables

4X^2-30=0

a = 4; b = 0; c = -30;
Δ = b2-4ac
Δ = 02-4·4·(-30)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{30}}{2*4}=\frac{0-4\sqrt{30}}{8}
=-\frac{4\sqrt{30}}{8}
=-\frac{\sqrt{30}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{30}}{2*4}=\frac{0+4\sqrt{30}}{8}
=\frac{4\sqrt{30}}{8}
=\frac{\sqrt{30}}{2}
$