2/x=3x+1

Solution for 2/x=3x+1 equation:

2/x=3x+1

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We get rid of parentheses

2/x-3x-1=0

We multiply all the terms by the denominator


-3x*x-1*x+2=0

We add all the numbers together, and all the variables

-1x-3x*x+2=0

Wy multiply elements

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

a = -3; b = -1; c = +2;
Δ = b2-4ac
Δ = -12-4·(-3)·2
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{-(-1)-5}{2*-3}=\frac{-4}{-6}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5}{2*-3}=\frac{6}{-6}
=-1
$