x^2=38-x^2

Solution for x^2=38-x^2 equation:

x^2=38-x^2

We move all terms to the left:

x^2-(38-x^2)=0

We get rid of parentheses

x^2+x^2-38=0

We add all the numbers together, and all the variables

2x^2-38=0

a = 2; b = 0; c = -38;
Δ = b2-4ac
Δ = 02-4·2·(-38)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{19}}{2*2}=\frac{0-4\sqrt{19}}{4}
=-\frac{4\sqrt{19}}{4}
=-\sqrt{19}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{19}}{2*2}=\frac{0+4\sqrt{19}}{4}
=\frac{4\sqrt{19}}{4}
=\sqrt{19}
$