X2+4y2=37

Solution for X2+4y2=37 equation:

X2+4X^2=37

We move all terms to the left:

X2+4X^2-(37)=0

We add all the numbers together, and all the variables

5X^2-37=0

a = 5; b = 0; c = -37;
Δ = b2-4ac
Δ = 02-4·5·(-37)
Δ = 740
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:

$\sqrt{\Delta}=\sqrt{740}=\sqrt{4*185}=\sqrt{4}*\sqrt{185}=2\sqrt{185}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{185}}{2*5}=\frac{0-2\sqrt{185}}{10}
=-\frac{2\sqrt{185}}{10}
=-\frac{\sqrt{185}}{5}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{185}}{2*5}=\frac{0+2\sqrt{185}}{10}
=\frac{2\sqrt{185}}{10}
=\frac{\sqrt{185}}{5}
$