3/2x+3=4/5x

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

3/2x+3=4/5x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


15x/10x^2+(-8x)/10x^2+3=0

We multiply all the terms by the denominator


15x+(-8x)+3*10x^2=0

Wy multiply elements

30x^2+15x+(-8x)=0

We get rid of parentheses

30x^2+15x-8x=0

We add all the numbers together, and all the variables

30x^2+7x=0

a = 30; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·30·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*30}=\frac{-14}{60}
=-7/30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*30}=\frac{0}{60}
=0
$