x^2=64/343

Solution for x^2=64/343 equation:

x^2=64/343

We move all terms to the left:

x^2-(64/343)=0

We add all the numbers together, and all the variables

x^2-(+64/343)=0

We get rid of parentheses

x^2-64/343=0

We multiply all the terms by the denominator


x^2*343-64=0

Wy multiply elements

343x^2-64=0

a = 343; b = 0; c = -64;
Δ = b2-4ac
Δ = 02-4·343·(-64)
Δ = 87808
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:

$\sqrt{\Delta}=\sqrt{87808}=\sqrt{12544*7}=\sqrt{12544}*\sqrt{7}=112\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-112\sqrt{7}}{2*343}=\frac{0-112\sqrt{7}}{686}
=-\frac{112\sqrt{7}}{686}
=-\frac{8\sqrt{7}}{49}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+112\sqrt{7}}{2*343}=\frac{0+112\sqrt{7}}{686}
=\frac{112\sqrt{7}}{686}
=\frac{8\sqrt{7}}{49}
$