X2+4y2=100

Solution for X2+4y2=100 equation:

X2+4X^2=100

We move all terms to the left:

X2+4X^2-(100)=0

We add all the numbers together, and all the variables

5X^2-100=0

a = 5; b = 0; c = -100;
Δ = b2-4ac
Δ = 02-4·5·(-100)
Δ = 2000
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:

$\sqrt{\Delta}=\sqrt{2000}=\sqrt{400*5}=\sqrt{400}*\sqrt{5}=20\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{5}}{2*5}=\frac{0-20\sqrt{5}}{10}
=-\frac{20\sqrt{5}}{10}
=-2\sqrt{5}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{5}}{2*5}=\frac{0+20\sqrt{5}}{10}
=\frac{20\sqrt{5}}{10}
=2\sqrt{5}
$