4/x=3x+1

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

4/x=3x+1

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We get rid of parentheses

4/x-3x-1=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

-3x^2-1x+4=0

a = -3; b = -1; c = +4;
Δ = b2-4ac
Δ = -12-4·(-3)·4
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*-3}=\frac{-6}{-6}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+7}{2*-3}=\frac{8}{-6}
=-1+1/3
$