x^2+x^2=5184

Solution for x^2+x^2=5184 equation:

x^2+x^2=5184

We move all terms to the left:

x^2+x^2-(5184)=0

We add all the numbers together, and all the variables

2x^2-5184=0

a = 2; b = 0; c = -5184;
Δ = b2-4ac
Δ = 02-4·2·(-5184)
Δ = 41472
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:

$\sqrt{\Delta}=\sqrt{41472}=\sqrt{20736*2}=\sqrt{20736}*\sqrt{2}=144\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-144\sqrt{2}}{2*2}=\frac{0-144\sqrt{2}}{4}
=-\frac{144\sqrt{2}}{4}
=-36\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+144\sqrt{2}}{2*2}=\frac{0+144\sqrt{2}}{4}
=\frac{144\sqrt{2}}{4}
=36\sqrt{2}
$