4x+1=1/3x

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

4x+1=1/3x

We move all terms to the left:

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


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

4x-1/3x+1=0

We multiply all the terms by the denominator


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

Wy multiply elements

12x^2+3x-1=0

a = 12; b = 3; c = -1;
Δ = b2-4ac
Δ = 32-4·12·(-1)
Δ = 57
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{-(3)-\sqrt{57}}{2*12}=\frac{-3-\sqrt{57}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{57}}{2*12}=\frac{-3+\sqrt{57}}{24}
$