1-(1/x)=-5x

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

1-(1/x)=-5x

We move all terms to the left:

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


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-1/x+5x+1=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

x+5x*x-1=0

Wy multiply elements

5x^2+x-1=0

a = 5; b = 1; c = -1;
Δ = b2-4ac
Δ = 12-4·5·(-1)
Δ = 21
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{21}}{2*5}=\frac{-1-\sqrt{21}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{21}}{2*5}=\frac{-1+\sqrt{21}}{10}
$