2X^2+2y^2+2Z^2=50

Solution for 2X^2+2y^2+2Z^2=50 equation:

2X^2+2X^2+2^2=50

We move all terms to the left:

2X^2+2X^2+2^2-(50)=0

determiningTheFunctionDomain
2X^2+2X^2-50+2^2=0

We add all the numbers together, and all the variables

4X^2-46=0

a = 4; b = 0; c = -46;
Δ = b2-4ac
Δ = 02-4·4·(-46)
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{46}}{2*4}=\frac{0-4\sqrt{46}}{8}
=-\frac{4\sqrt{46}}{8}
=-\frac{\sqrt{46}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{46}}{2*4}=\frac{0+4\sqrt{46}}{8}
=\frac{4\sqrt{46}}{8}
=\frac{\sqrt{46}}{2}
$