x*2,3^2=2/3

Solution for x*2,3^2=2/3 equation:

x*2.3^2=2/3

We move all terms to the left:

x*2.3^2-(2/3)=0

We add all the numbers together, and all the variables

x*2.3^2-(+2/3)=0

Wy multiply elements

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

We get rid of parentheses

2x^2-2/3=0

We multiply all the terms by the denominator


2x^2*3-2=0

Wy multiply elements

6x^2-2=0

a = 6; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·6·(-2)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{3}}{2*6}=\frac{0-4\sqrt{3}}{12}
=-\frac{4\sqrt{3}}{12}
=-\frac{\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{3}}{2*6}=\frac{0+4\sqrt{3}}{12}
=\frac{4\sqrt{3}}{12}
=\frac{\sqrt{3}}{3}
$