X^2=39-x^2

Solution for X^2=39-x^2 equation:

X^2=39-X^2

We move all terms to the left:

X^2-(39-X^2)=0

We get rid of parentheses

X^2+X^2-39=0

We add all the numbers together, and all the variables

2X^2-39=0

a = 2; b = 0; c = -39;
Δ = b2-4ac
Δ = 02-4·2·(-39)
Δ = 312
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:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{78}}{2*2}=\frac{0-2\sqrt{78}}{4}
=-\frac{2\sqrt{78}}{4}
=-\frac{\sqrt{78}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{78}}{2*2}=\frac{0+2\sqrt{78}}{4}
=\frac{2\sqrt{78}}{4}
=\frac{\sqrt{78}}{2}
$