3/2x+5=7/3x+1

Solution for 3/2x+5=7/3x+1 equation:

3/2x+5=7/3x+1

We move all terms to the left:

3/2x+5-(7/3x+1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x+1)!=0

x∈R


We get rid of parentheses

3/2x-7/3x-1+5=0

We calculate fractions


9x/6x^2+(-14x)/6x^2-1+5=0

We add all the numbers together, and all the variables

9x/6x^2+(-14x)/6x^2+4=0

We multiply all the terms by the denominator


9x+(-14x)+4*6x^2=0

Wy multiply elements

24x^2+9x+(-14x)=0

We get rid of parentheses

24x^2+9x-14x=0

We add all the numbers together, and all the variables

24x^2-5x=0

a = 24; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·24·0
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*24}=\frac{0}{48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*24}=\frac{10}{48}
=5/24
$