X^2+4y^2=15

Solution for X^2+4y^2=15 equation:

X^2+4X^2=15

We move all terms to the left:

X^2+4X^2-(15)=0

We add all the numbers together, and all the variables

5X^2-15=0

a = 5; b = 0; c = -15;
Δ = b2-4ac
Δ = 02-4·5·(-15)
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{3}}{2*5}=\frac{0-10\sqrt{3}}{10}
=-\frac{10\sqrt{3}}{10}
=-\sqrt{3}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{3}}{2*5}=\frac{0+10\sqrt{3}}{10}
=\frac{10\sqrt{3}}{10}
=\sqrt{3}
$