X2+y2=1989

Solution for X2+y2=1989 equation:

X2+X2=1989

We move all terms to the left:

X2+X2-(1989)=0

We add all the numbers together, and all the variables

2X^2-1989=0

a = 2; b = 0; c = -1989;
Δ = b2-4ac
Δ = 02-4·2·(-1989)
Δ = 15912
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:

$\sqrt{\Delta}=\sqrt{15912}=\sqrt{36*442}=\sqrt{36}*\sqrt{442}=6\sqrt{442}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{442}}{2*2}=\frac{0-6\sqrt{442}}{4}
=-\frac{6\sqrt{442}}{4}
=-\frac{3\sqrt{442}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{442}}{2*2}=\frac{0+6\sqrt{442}}{4}
=\frac{6\sqrt{442}}{4}
=\frac{3\sqrt{442}}{2}
$