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

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

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

We move all terms to the left:

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


Domain of the equation: 31x!=0

x!=0/31

x!=0

x∈R


We get rid of parentheses

2/31x-3x-1=0

We multiply all the terms by the denominator


-3x*31x-1*31x+2=0

Wy multiply elements

-93x^2-31x+2=0

a = -93; b = -31; c = +2;
Δ = b2-4ac
Δ = -312-4·(-93)·2
Δ = 1705
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{-(-31)-\sqrt{1705}}{2*-93}=\frac{31-\sqrt{1705}}{-186}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{1705}}{2*-93}=\frac{31+\sqrt{1705}}{-186}
$