7x^2-3Y^2=2

Solution for 7x^2-3Y^2=2 equation:

7x^2-3^2=2

We move all terms to the left:

7x^2-3^2-(2)=0

determiningTheFunctionDomain
7x^2-2-3^2=0

We add all the numbers together, and all the variables

7x^2-11=0

a = 7; b = 0; c = -11;
Δ = b2-4ac
Δ = 02-4·7·(-11)
Δ = 308
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:

$\sqrt{\Delta}=\sqrt{308}=\sqrt{4*77}=\sqrt{4}*\sqrt{77}=2\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{77}}{2*7}=\frac{0-2\sqrt{77}}{14}
=-\frac{2\sqrt{77}}{14}
=-\frac{\sqrt{77}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{77}}{2*7}=\frac{0+2\sqrt{77}}{14}
=\frac{2\sqrt{77}}{14}
=\frac{\sqrt{77}}{7}
$