2/3(x)=3x+1

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

2/3(x)=3x+1

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-3x-1=0

We multiply all the terms by the denominator


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

Wy multiply elements

-9x^2-3x+2=0

a = -9; b = -3; c = +2;
Δ = b2-4ac
Δ = -32-4·(-9)·2
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-9}{2*-9}=\frac{-6}{-18}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+9}{2*-9}=\frac{12}{-18}
=-2/3
$