4*x^2=576*3+x^2

Solution for 4*x^2=576*3+x^2 equation:

4*x^2=576*3+x^2

We move all terms to the left:

4*x^2-(576*3+x^2)=0

We add all the numbers together, and all the variables

4x^2-(576*3+x^2)=0

We get rid of parentheses

4x^2-x^2-576*3=0

We add all the numbers together, and all the variables

3x^2-1728=0

a = 3; b = 0; c = -1728;
Δ = b2-4ac
Δ = 02-4·3·(-1728)
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-144}{2*3}=\frac{-144}{6}
=-24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+144}{2*3}=\frac{144}{6}
=24
$