X^2+2y^2=11

Solution for X^2+2y^2=11 equation:

X^2+2X^2=11

We move all terms to the left:

X^2+2X^2-(11)=0

We add all the numbers together, and all the variables

3X^2-11=0

a = 3; b = 0; c = -11;
Δ = b2-4ac
Δ = 02-4·3·(-11)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{33}}{2*3}=\frac{0-2\sqrt{33}}{6}
=-\frac{2\sqrt{33}}{6}
=-\frac{\sqrt{33}}{3}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{33}}{2*3}=\frac{0+2\sqrt{33}}{6}
=\frac{2\sqrt{33}}{6}
=\frac{\sqrt{33}}{3}
$