x^2=5/529

Solution for x^2=5/529 equation:

x^2=5/529

We move all terms to the left:

x^2-(5/529)=0

We add all the numbers together, and all the variables

x^2-(+5/529)=0

We get rid of parentheses

x^2-5/529=0

We multiply all the terms by the denominator


x^2*529-5=0

Wy multiply elements

529x^2-5=0

a = 529; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·529·(-5)
Δ = 10580
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:

$\sqrt{\Delta}=\sqrt{10580}=\sqrt{2116*5}=\sqrt{2116}*\sqrt{5}=46\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-46\sqrt{5}}{2*529}=\frac{0-46\sqrt{5}}{1058}
=-\frac{46\sqrt{5}}{1058}
=-\frac{\sqrt{5}}{23}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+46\sqrt{5}}{2*529}=\frac{0+46\sqrt{5}}{1058}
=\frac{46\sqrt{5}}{1058}
=\frac{\sqrt{5}}{23}
$