(1/3)x-5=x/5

Solution for (1/3)x-5=x/5 equation:

(1/3)x-5=x/5

We move all terms to the left:

(1/3)x-5-(x/5)=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/3)x-(+x/5)-5=0

We multiply parentheses

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

We get rid of parentheses

x^2-x/5-5=0

We multiply all the terms by the denominator


x^2*5-x-5*5=0

We add all the numbers together, and all the variables

x^2*5-1x-25=0

Wy multiply elements

5x^2-1x-25=0

a = 5; b = -1; c = -25;
Δ = b2-4ac
Δ = -12-4·5·(-25)
Δ = 501
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{501}}{2*5}=\frac{1-\sqrt{501}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{501}}{2*5}=\frac{1+\sqrt{501}}{10}
$