1/5x=5-x

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

1/5x=5-x

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/5x+1x-5=0

We multiply all the terms by the denominator


1x*5x-5*5x+1=0

Wy multiply elements

5x^2-25x+1=0

a = 5; b = -25; c = +1;
Δ = b2-4ac
Δ = -252-4·5·1
Δ = 605
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:

$\sqrt{\Delta}=\sqrt{605}=\sqrt{121*5}=\sqrt{121}*\sqrt{5}=11\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-11\sqrt{5}}{2*5}=\frac{25-11\sqrt{5}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+11\sqrt{5}}{2*5}=\frac{25+11\sqrt{5}}{10}
$