4x-(1/x)=3

Solution for 4x-(1/x)=3 equation:

4x-(1/x)=3

We move all terms to the left:

4x-(1/x)-(3)=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)-3=0

We get rid of parentheses

4x-1/x-3=0

We multiply all the terms by the denominator


4x*x-3*x-1=0

We add all the numbers together, and all the variables

-3x+4x*x-1=0

Wy multiply elements

4x^2-3x-1=0

a = 4; b = -3; c = -1;
Δ = b2-4ac
Δ = -32-4·4·(-1)
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{-(-3)-5}{2*4}=\frac{-2}{8}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+5}{2*4}=\frac{8}{8}
=1
$