X^2/3+4y^2=1

Solution for X^2/3+4y^2=1 equation:

X^2/3+4X^2=1

We move all terms to the left:

X^2/3+4X^2-(1)=0

We add all the numbers together, and all the variables

4X^2+X^2/3-1=0

We multiply all the terms by the denominator


X^2+4X^2*3-1*3=0

We add all the numbers together, and all the variables

X^2+4X^2*3-3=0

Wy multiply elements

X^2+12X^2-3=0

We add all the numbers together, and all the variables

13X^2-3=0

a = 13; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·13·(-3)
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{39}}{2*13}=\frac{0-2\sqrt{39}}{26}
=-\frac{2\sqrt{39}}{26}
=-\frac{\sqrt{39}}{13}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{39}}{2*13}=\frac{0+2\sqrt{39}}{26}
=\frac{2\sqrt{39}}{26}
=\frac{\sqrt{39}}{13}
$