1/5=x/x^2

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

1/5=x/x^2

We move all terms to the left:

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


Domain of the equation: x^2)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


x^2+(-5x)=0

We get rid of parentheses

x^2-5x=0

a = 1; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·1·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*1}=\frac{10}{2}
=5
$