5x-(1/x)=-4

Solution for 5x-(1/x)=-4 equation:

5x-(1/x)=-4

We move all terms to the left:

5x-(1/x)-(-4)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x-(+1/x)-(-4)=0

We add all the numbers together, and all the variables

5x-(+1/x)+4=0

We get rid of parentheses

5x-1/x+4=0

We multiply all the terms by the denominator


5x*x+4*x-1=0

We add all the numbers together, and all the variables

4x+5x*x-1=0

Wy multiply elements

5x^2+4x-1=0

a = 5; b = 4; c = -1;
Δ = b2-4ac
Δ = 42-4·5·(-1)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-6}{2*5}=\frac{-10}{10}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+6}{2*5}=\frac{2}{10}
=1/5
$