6x^2/3-216=0

Solution for 6x^2/3-216=0 equation:

6x^2/3-216=0

We multiply all the terms by the denominator


6x^2-216*3=0

We add all the numbers together, and all the variables

6x^2-648=0

a = 6; b = 0; c = -648;
Δ = b2-4ac
Δ = 02-4·6·(-648)
Δ = 15552
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:

$\sqrt{\Delta}=\sqrt{15552}=\sqrt{5184*3}=\sqrt{5184}*\sqrt{3}=72\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72\sqrt{3}}{2*6}=\frac{0-72\sqrt{3}}{12}
=-\frac{72\sqrt{3}}{12}
=-6\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72\sqrt{3}}{2*6}=\frac{0+72\sqrt{3}}{12}
=\frac{72\sqrt{3}}{12}
=6\sqrt{3}
$