X^2+4y^2=3600

Solution for X^2+4y^2=3600 equation:

X^2+4X^2=3600

We move all terms to the left:

X^2+4X^2-(3600)=0

We add all the numbers together, and all the variables

5X^2-3600=0

a = 5; b = 0; c = -3600;
Δ = b2-4ac
Δ = 02-4·5·(-3600)
Δ = 72000
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:

$\sqrt{\Delta}=\sqrt{72000}=\sqrt{14400*5}=\sqrt{14400}*\sqrt{5}=120\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-120\sqrt{5}}{2*5}=\frac{0-120\sqrt{5}}{10}
=-\frac{120\sqrt{5}}{10}
=-12\sqrt{5}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+120\sqrt{5}}{2*5}=\frac{0+120\sqrt{5}}{10}
=\frac{120\sqrt{5}}{10}
=12\sqrt{5}
$