X^2+2x^2=6400

Solution for X^2+2x^2=6400 equation:

X^2+2X^2=6400

We move all terms to the left:

X^2+2X^2-(6400)=0

We add all the numbers together, and all the variables

3X^2-6400=0

a = 3; b = 0; c = -6400;
Δ = b2-4ac
Δ = 02-4·3·(-6400)
Δ = 76800
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:

$\sqrt{\Delta}=\sqrt{76800}=\sqrt{25600*3}=\sqrt{25600}*\sqrt{3}=160\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-160\sqrt{3}}{2*3}=\frac{0-160\sqrt{3}}{6}
=-\frac{160\sqrt{3}}{6}
=-\frac{80\sqrt{3}}{3}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+160\sqrt{3}}{2*3}=\frac{0+160\sqrt{3}}{6}
=\frac{160\sqrt{3}}{6}
=\frac{80\sqrt{3}}{3}
$