5x^2=5184-x^2

Solution for 5x^2=5184-x^2 equation:

5x^2=5184-x^2

We move all terms to the left:

5x^2-(5184-x^2)=0

We get rid of parentheses

5x^2+x^2-5184=0

We add all the numbers together, and all the variables

6x^2-5184=0

a = 6; b = 0; c = -5184;
Δ = b2-4ac
Δ = 02-4·6·(-5184)
Δ = 124416
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:

$\sqrt{\Delta}=\sqrt{124416}=\sqrt{20736*6}=\sqrt{20736}*\sqrt{6}=144\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-144\sqrt{6}}{2*6}=\frac{0-144\sqrt{6}}{12}
=-\frac{144\sqrt{6}}{12}
=-12\sqrt{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+144\sqrt{6}}{2*6}=\frac{0+144\sqrt{6}}{12}
=\frac{144\sqrt{6}}{12}
=12\sqrt{6}
$