4/3x-2=5-2x

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

4/3x-2=5-2x

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

4/3x+2x-5-2=0

We multiply all the terms by the denominator


2x*3x-5*3x-2*3x+4=0

Wy multiply elements

6x^2-15x-6x+4=0

We add all the numbers together, and all the variables

6x^2-21x+4=0

a = 6; b = -21; c = +4;
Δ = b2-4ac
Δ = -212-4·6·4
Δ = 345
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{345}}{2*6}=\frac{21-\sqrt{345}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{345}}{2*6}=\frac{21+\sqrt{345}}{12}
$