4x+1=3/x

Solution for 4x+1=3/x equation:

4x+1=3/x

We move all terms to the left:

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

We get rid of parentheses

4x-3/x+1=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

x+4x*x-3=0

Wy multiply elements

4x^2+x-3=0

a = 4; b = 1; c = -3;
Δ = b2-4ac
Δ = 12-4·4·(-3)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-7}{2*4}=\frac{-8}{8}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+7}{2*4}=\frac{6}{8}
=3/4
$