0=4x-1/x

Solution for 0=4x-1/x equation:

0=4x-1/x

We move all terms to the left:

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


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-4x+1/x=0

We multiply all the terms by the denominator


-4x*x+1=0

Wy multiply elements

-4x^2+1=0

a = -4; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-4)·1
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4}{2*-4}=\frac{-4}{-8}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4}{2*-4}=\frac{4}{-8}
=-1/2
$