X^2+y^2=84

Solution for X^2+y^2=84 equation:

X^2+X^2=84

We move all terms to the left:

X^2+X^2-(84)=0

We add all the numbers together, and all the variables

2X^2-84=0

a = 2; b = 0; c = -84;
Δ = b2-4ac
Δ = 02-4·2·(-84)
Δ = 672
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:

$\sqrt{\Delta}=\sqrt{672}=\sqrt{16*42}=\sqrt{16}*\sqrt{42}=4\sqrt{42}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{42}}{2*2}=\frac{0-4\sqrt{42}}{4}
=-\frac{4\sqrt{42}}{4}
=-\sqrt{42}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{42}}{2*2}=\frac{0+4\sqrt{42}}{4}
=\frac{4\sqrt{42}}{4}
=\sqrt{42}
$