X^2+y^2=2018

Solution for X^2+y^2=2018 equation:

X^2+X^2=2018

We move all terms to the left:

X^2+X^2-(2018)=0

We add all the numbers together, and all the variables

2X^2-2018=0

a = 2; b = 0; c = -2018;
Δ = b2-4ac
Δ = 02-4·2·(-2018)
Δ = 16144
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:

$\sqrt{\Delta}=\sqrt{16144}=\sqrt{16*1009}=\sqrt{16}*\sqrt{1009}=4\sqrt{1009}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{1009}}{2*2}=\frac{0-4\sqrt{1009}}{4}
=-\frac{4\sqrt{1009}}{4}
=-\sqrt{1009}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{1009}}{2*2}=\frac{0+4\sqrt{1009}}{4}
=\frac{4\sqrt{1009}}{4}
=\sqrt{1009}
$