2/3x+5=3/2x

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

2/3x+5=3/2x

We move all terms to the left:

2/3x+5-(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

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

We get rid of parentheses

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

We calculate fractions


4x/6x^2+(-9x)/6x^2+5=0

We multiply all the terms by the denominator


4x+(-9x)+5*6x^2=0

Wy multiply elements

30x^2+4x+(-9x)=0

We get rid of parentheses

30x^2+4x-9x=0

We add all the numbers together, and all the variables

30x^2-5x=0

a = 30; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·30·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*30}=\frac{0}{60}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*30}=\frac{10}{60}
=1/6
$