x^2=100/125

Solution for x^2=100/125 equation:

x^2=100/125

We move all terms to the left:

x^2-(100/125)=0

We add all the numbers together, and all the variables

x^2-(+100/125)=0

We get rid of parentheses

x^2-100/125=0

We multiply all the terms by the denominator


x^2*125-100=0

Wy multiply elements

125x^2-100=0

a = 125; b = 0; c = -100;
Δ = b2-4ac
Δ = 02-4·125·(-100)
Δ = 50000
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:

$\sqrt{\Delta}=\sqrt{50000}=\sqrt{10000*5}=\sqrt{10000}*\sqrt{5}=100\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100\sqrt{5}}{2*125}=\frac{0-100\sqrt{5}}{250}
=-\frac{100\sqrt{5}}{250}
=-\frac{2\sqrt{5}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100\sqrt{5}}{2*125}=\frac{0+100\sqrt{5}}{250}
=\frac{100\sqrt{5}}{250}
=\frac{2\sqrt{5}}{5}
$