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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 3x+3)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-2x*3x-3*3x+7=0

Wy multiply elements

-6x^2-9x+7=0

a = -6; b = -9; c = +7;
Δ = b2-4ac
Δ = -92-4·(-6)·7
Δ = 249
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{-(-9)-\sqrt{249}}{2*-6}=\frac{9-\sqrt{249}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{249}}{2*-6}=\frac{9+\sqrt{249}}{-12}
$