5/3x=6-3/2x

Solution for 5/3x=6-3/2x equation:

5/3x=6-3/2x

We move all terms to the left:

5/3x-(6-3/2x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/3x-(-3/2x+6)=0

We get rid of parentheses

5/3x+3/2x-6=0

We calculate fractions


10x/6x^2+9x/6x^2-6=0

We multiply all the terms by the denominator


10x+9x-6*6x^2=0

We add all the numbers together, and all the variables

19x-6*6x^2=0

Wy multiply elements

-36x^2+19x=0

a = -36; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-36)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-36}=\frac{-38}{-72}
=19/36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-36}=\frac{0}{-72}
=0
$