x^2=8/729

Solution for x^2=8/729 equation:

x^2=8/729

We move all terms to the left:

x^2-(8/729)=0

We add all the numbers together, and all the variables

x^2-(+8/729)=0

We get rid of parentheses

x^2-8/729=0

We multiply all the terms by the denominator


x^2*729-8=0

Wy multiply elements

729x^2-8=0

a = 729; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·729·(-8)
Δ = 23328
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:

$\sqrt{\Delta}=\sqrt{23328}=\sqrt{11664*2}=\sqrt{11664}*\sqrt{2}=108\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-108\sqrt{2}}{2*729}=\frac{0-108\sqrt{2}}{1458}
=-\frac{108\sqrt{2}}{1458}
=-\frac{2\sqrt{2}}{27}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+108\sqrt{2}}{2*729}=\frac{0+108\sqrt{2}}{1458}
=\frac{108\sqrt{2}}{1458}
=\frac{2\sqrt{2}}{27}
$