x^2+(X^2+1)=394

Solution for x^2+(X^2+1)=394 equation:

x^2+(x^2+1)=394

We move all terms to the left:

x^2+(x^2+1)-(394)=0

We get rid of parentheses

x^2+x^2+1-394=0

We add all the numbers together, and all the variables

2x^2-393=0

a = 2; b = 0; c = -393;
Δ = b2-4ac
Δ = 02-4·2·(-393)
Δ = 3144
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:

$\sqrt{\Delta}=\sqrt{3144}=\sqrt{4*786}=\sqrt{4}*\sqrt{786}=2\sqrt{786}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{786}}{2*2}=\frac{0-2\sqrt{786}}{4}
=-\frac{2\sqrt{786}}{4}
=-\frac{\sqrt{786}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{786}}{2*2}=\frac{0+2\sqrt{786}}{4}
=\frac{2\sqrt{786}}{4}
=\frac{\sqrt{786}}{2}
$