2/3x^2=324

Solution for 2/3x^2=324 equation:

2/3x^2=324

We move all terms to the left:

2/3x^2-(324)=0


Domain of the equation: 3x^2!=0

x^2!=0/3

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


-324*3x^2+2=0

Wy multiply elements

-972x^2+2=0

a = -972; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-972)·2
Δ = 7776
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:

$\sqrt{\Delta}=\sqrt{7776}=\sqrt{1296*6}=\sqrt{1296}*\sqrt{6}=36\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{6}}{2*-972}=\frac{0-36\sqrt{6}}{-1944}
=-\frac{36\sqrt{6}}{-1944}
=-\frac{\sqrt{6}}{-54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{6}}{2*-972}=\frac{0+36\sqrt{6}}{-1944}
=\frac{36\sqrt{6}}{-1944}
=\frac{\sqrt{6}}{-54}
$