x^2=8/27

Solution for x^2=8/27 equation:

x^2=8/27

We move all terms to the left:

x^2-(8/27)=0

We add all the numbers together, and all the variables

x^2-(+8/27)=0

We get rid of parentheses

x^2-8/27=0

We multiply all the terms by the denominator


x^2*27-8=0

Wy multiply elements

27x^2-8=0

a = 27; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·27·(-8)
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{6}}{2*27}=\frac{0-12\sqrt{6}}{54}
=-\frac{12\sqrt{6}}{54}
=-\frac{2\sqrt{6}}{9}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{6}}{2*27}=\frac{0+12\sqrt{6}}{54}
=\frac{12\sqrt{6}}{54}
=\frac{2\sqrt{6}}{9}
$