x^2+2x^2=210^2

Solution for x^2+2x^2=210^2 equation:

x^2+2x^2=210^2

We move all terms to the left:

x^2+2x^2-(210^2)=0

We add all the numbers together, and all the variables

3x^2-44100=0

a = 3; b = 0; c = -44100;
Δ = b2-4ac
Δ = 02-4·3·(-44100)
Δ = 529200
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:

$\sqrt{\Delta}=\sqrt{529200}=\sqrt{176400*3}=\sqrt{176400}*\sqrt{3}=420\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-420\sqrt{3}}{2*3}=\frac{0-420\sqrt{3}}{6}
=-\frac{420\sqrt{3}}{6}
=-70\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+420\sqrt{3}}{2*3}=\frac{0+420\sqrt{3}}{6}
=\frac{420\sqrt{3}}{6}
=70\sqrt{3}
$