x^2=2/27

Solution for x^2=2/27 equation:

x^2=2/27

We move all terms to the left:

x^2-(2/27)=0

We add all the numbers together, and all the variables

x^2-(+2/27)=0

We get rid of parentheses

x^2-2/27=0

We multiply all the terms by the denominator


x^2*27-2=0

Wy multiply elements

27x^2-2=0

a = 27; b = 0; c = -2;
Δ = b2-4ac
Δ = 02-4·27·(-2)
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{6}}{2*27}=\frac{0-6\sqrt{6}}{54}
=-\frac{6\sqrt{6}}{54}
=-\frac{\sqrt{6}}{9}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{6}}{2*27}=\frac{0+6\sqrt{6}}{54}
=\frac{6\sqrt{6}}{54}
=\frac{\sqrt{6}}{9}
$