5X^2+5y^2=125

Solution for 5X^2+5y^2=125 equation:

5X^2+5X^2=125

We move all terms to the left:

5X^2+5X^2-(125)=0

We add all the numbers together, and all the variables

10X^2-125=0

a = 10; b = 0; c = -125;
Δ = b2-4ac
Δ = 02-4·10·(-125)
Δ = 5000
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:

$\sqrt{\Delta}=\sqrt{5000}=\sqrt{2500*2}=\sqrt{2500}*\sqrt{2}=50\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-50\sqrt{2}}{2*10}=\frac{0-50\sqrt{2}}{20}
=-\frac{50\sqrt{2}}{20}
=-\frac{5\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+50\sqrt{2}}{2*10}=\frac{0+50\sqrt{2}}{20}
=\frac{50\sqrt{2}}{20}
=\frac{5\sqrt{2}}{2}
$