x^2=343/729

Solution for x^2=343/729 equation:

x^2=343/729

We move all terms to the left:

x^2-(343/729)=0

We add all the numbers together, and all the variables

x^2-(+343/729)=0

We get rid of parentheses

x^2-343/729=0

We multiply all the terms by the denominator


x^2*729-343=0

Wy multiply elements

729x^2-343=0

a = 729; b = 0; c = -343;
Δ = b2-4ac
Δ = 02-4·729·(-343)
Δ = 1000188
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:

$\sqrt{\Delta}=\sqrt{1000188}=\sqrt{142884*7}=\sqrt{142884}*\sqrt{7}=378\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-378\sqrt{7}}{2*729}=\frac{0-378\sqrt{7}}{1458}
=-\frac{378\sqrt{7}}{1458}
=-\frac{7\sqrt{7}}{27}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+378\sqrt{7}}{2*729}=\frac{0+378\sqrt{7}}{1458}
=\frac{378\sqrt{7}}{1458}
=\frac{7\sqrt{7}}{27}
$