x^2+2x^2=123

Solution for x^2+2x^2=123 equation:

x^2+2x^2=123

We move all terms to the left:

x^2+2x^2-(123)=0

We add all the numbers together, and all the variables

3x^2-123=0

a = 3; b = 0; c = -123;
Δ = b2-4ac
Δ = 02-4·3·(-123)
Δ = 1476
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:

$\sqrt{\Delta}=\sqrt{1476}=\sqrt{36*41}=\sqrt{36}*\sqrt{41}=6\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{41}}{2*3}=\frac{0-6\sqrt{41}}{6}
=-\frac{6\sqrt{41}}{6}
=-\sqrt{41}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{41}}{2*3}=\frac{0+6\sqrt{41}}{6}
=\frac{6\sqrt{41}}{6}
=\sqrt{41}
$