X2+y2=280

Solution for X2+y2=280 equation:

X2+X2=280

We move all terms to the left:

X2+X2-(280)=0

We add all the numbers together, and all the variables

2X^2-280=0

a = 2; b = 0; c = -280;
Δ = b2-4ac
Δ = 02-4·2·(-280)
Δ = 2240
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:

$\sqrt{\Delta}=\sqrt{2240}=\sqrt{64*35}=\sqrt{64}*\sqrt{35}=8\sqrt{35}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{35}}{2*2}=\frac{0-8\sqrt{35}}{4}
=-\frac{8\sqrt{35}}{4}
=-2\sqrt{35}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{35}}{2*2}=\frac{0+8\sqrt{35}}{4}
=\frac{8\sqrt{35}}{4}
=2\sqrt{35}
$