1/5x=x-2/5x

Solution for 1/5x=x-2/5x equation:

1/5x=x-2/5x

We move all terms to the left:

1/5x-(x-2/5x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/5x-(+x-2/5x)=0

We get rid of parentheses

1/5x-x+2/5x=0

We multiply all the terms by the denominator


-x*5x+1+2=0

We add all the numbers together, and all the variables

-x*5x+3=0

Wy multiply elements

-5x^2+3=0

a = -5; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-5)·3
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{15}}{2*-5}=\frac{0-2\sqrt{15}}{-10}
=-\frac{2\sqrt{15}}{-10}
=-\frac{\sqrt{15}}{-5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{15}}{2*-5}=\frac{0+2\sqrt{15}}{-10}
=\frac{2\sqrt{15}}{-10}
=\frac{\sqrt{15}}{-5}
$