(2/5)x=8/125

Solution for (2/5)x=8/125 equation:

(2/5)x=8/125

We move all terms to the left:

(2/5)x-(8/125)=0


Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+2/5)x-(+8/125)=0

We multiply parentheses

2x^2-(+8/125)=0

We get rid of parentheses

2x^2-8/125=0

We multiply all the terms by the denominator


2x^2*125-8=0

Wy multiply elements

250x^2-8=0

a = 250; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·250·(-8)
Δ = 8000
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:

$\sqrt{\Delta}=\sqrt{8000}=\sqrt{1600*5}=\sqrt{1600}*\sqrt{5}=40\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{5}}{2*250}=\frac{0-40\sqrt{5}}{500}
=-\frac{40\sqrt{5}}{500}
=-\frac{2\sqrt{5}}{25}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{5}}{2*250}=\frac{0+40\sqrt{5}}{500}
=\frac{40\sqrt{5}}{500}
=\frac{2\sqrt{5}}{25}
$