(x^2)+(2x^2)=12100

Solution for (x^2)+(2x^2)=12100 equation:

(x^2)+(2x^2)=12100

We move all terms to the left:

(x^2)+(2x^2)-(12100)=0

We add all the numbers together, and all the variables

3x^2-12100=0

a = 3; b = 0; c = -12100;
Δ = b2-4ac
Δ = 02-4·3·(-12100)
Δ = 145200
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:

$\sqrt{\Delta}=\sqrt{145200}=\sqrt{48400*3}=\sqrt{48400}*\sqrt{3}=220\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-220\sqrt{3}}{2*3}=\frac{0-220\sqrt{3}}{6}
=-\frac{220\sqrt{3}}{6}
=-\frac{110\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+220\sqrt{3}}{2*3}=\frac{0+220\sqrt{3}}{6}
=\frac{220\sqrt{3}}{6}
=\frac{110\sqrt{3}}{3}
$