2/3x-3-5=2x-4x-1

Solution for 2/3x-3-5=2x-4x-1 equation:

2/3x-3-5=2x-4x-1

We move all terms to the left:

2/3x-3-5-(2x-4x-1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(-2x-1)-3-5=0

We add all the numbers together, and all the variables

2/3x-(-2x-1)-8=0

We get rid of parentheses

2/3x+2x+1-8=0

We multiply all the terms by the denominator


2x*3x+1*3x-8*3x+2=0

Wy multiply elements

6x^2+3x-24x+2=0

We add all the numbers together, and all the variables

6x^2-21x+2=0

a = 6; b = -21; c = +2;
Δ = b2-4ac
Δ = -212-4·6·2
Δ = 393
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{-(-21)-\sqrt{393}}{2*6}=\frac{21-\sqrt{393}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{393}}{2*6}=\frac{21+\sqrt{393}}{12}
$