x^2+2x^2+4x^2=343

Solution for x^2+2x^2+4x^2=343 equation:

x^2+2x^2+4x^2=343

We move all terms to the left:

x^2+2x^2+4x^2-(343)=0

We add all the numbers together, and all the variables

7x^2-343=0

a = 7; b = 0; c = -343;
Δ = b2-4ac
Δ = 02-4·7·(-343)
Δ = 9604
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9604}=98$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-98}{2*7}=\frac{-98}{14}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+98}{2*7}=\frac{98}{14}
=7
$