X^2+4y^2=116

Solution for X^2+4y^2=116 equation:

X^2+4X^2=116

We move all terms to the left:

X^2+4X^2-(116)=0

We add all the numbers together, and all the variables

5X^2-116=0

a = 5; b = 0; c = -116;
Δ = b2-4ac
Δ = 02-4·5·(-116)
Δ = 2320
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:

$\sqrt{\Delta}=\sqrt{2320}=\sqrt{16*145}=\sqrt{16}*\sqrt{145}=4\sqrt{145}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{145}}{2*5}=\frac{0-4\sqrt{145}}{10}
=-\frac{4\sqrt{145}}{10}
=-\frac{2\sqrt{145}}{5}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{145}}{2*5}=\frac{0+4\sqrt{145}}{10}
=\frac{4\sqrt{145}}{10}
=\frac{2\sqrt{145}}{5}
$