x^2=27/125

Solution for x^2=27/125 equation:

x^2=27/125

We move all terms to the left:

x^2-(27/125)=0

We add all the numbers together, and all the variables

x^2-(+27/125)=0

We get rid of parentheses

x^2-27/125=0

We multiply all the terms by the denominator


x^2*125-27=0

Wy multiply elements

125x^2-27=0

a = 125; b = 0; c = -27;
Δ = b2-4ac
Δ = 02-4·125·(-27)
Δ = 13500
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:

$\sqrt{\Delta}=\sqrt{13500}=\sqrt{900*15}=\sqrt{900}*\sqrt{15}=30\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{15}}{2*125}=\frac{0-30\sqrt{15}}{250}
=-\frac{30\sqrt{15}}{250}
=-\frac{3\sqrt{15}}{25}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{15}}{2*125}=\frac{0+30\sqrt{15}}{250}
=\frac{30\sqrt{15}}{250}
=\frac{3\sqrt{15}}{25}
$