X^2+3y^2=43

Solution for X^2+3y^2=43 equation:

X^2+3X^2=43

We move all terms to the left:

X^2+3X^2-(43)=0

We add all the numbers together, and all the variables

4X^2-43=0

a = 4; b = 0; c = -43;
Δ = b2-4ac
Δ = 02-4·4·(-43)
Δ = 688
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:

$\sqrt{\Delta}=\sqrt{688}=\sqrt{16*43}=\sqrt{16}*\sqrt{43}=4\sqrt{43}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{43}}{2*4}=\frac{0-4\sqrt{43}}{8}
=-\frac{4\sqrt{43}}{8}
=-\frac{\sqrt{43}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{43}}{2*4}=\frac{0+4\sqrt{43}}{8}
=\frac{4\sqrt{43}}{8}
=\frac{\sqrt{43}}{2}
$