X2+4y2=61

Solution for X2+4y2=61 equation:

X2+4X^2=61

We move all terms to the left:

X2+4X^2-(61)=0

We add all the numbers together, and all the variables

5X^2-61=0

a = 5; b = 0; c = -61;
Δ = b2-4ac
Δ = 02-4·5·(-61)
Δ = 1220
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:

$\sqrt{\Delta}=\sqrt{1220}=\sqrt{4*305}=\sqrt{4}*\sqrt{305}=2\sqrt{305}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{305}}{2*5}=\frac{0-2\sqrt{305}}{10}
=-\frac{2\sqrt{305}}{10}
=-\frac{\sqrt{305}}{5}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{305}}{2*5}=\frac{0+2\sqrt{305}}{10}
=\frac{2\sqrt{305}}{10}
=\frac{\sqrt{305}}{5}
$