3^2/3=9x^2/3

Solution for 3^2/3=9x^2/3 equation:

3^2/3=9x^2/3

We move all terms to the left:

3^2/3-(9x^2/3)=0

We add all the numbers together, and all the variables

-(9x^2/3)+1=0

We get rid of parentheses

-9x^2/3+1=0

We multiply all the terms by the denominator


-9x^2+1*3=0

We add all the numbers together, and all the variables

-9x^2+3=0

a = -9; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-9)·3
Δ = 108
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:

$\sqrt{\Delta}=\sqrt{108}=\sqrt{36*3}=\sqrt{36}*\sqrt{3}=6\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{3}}{2*-9}=\frac{0-6\sqrt{3}}{-18}
=-\frac{6\sqrt{3}}{-18}
=-\frac{\sqrt{3}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{3}}{2*-9}=\frac{0+6\sqrt{3}}{-18}
=\frac{6\sqrt{3}}{-18}
=\frac{\sqrt{3}}{-3}
$