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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


3x/2x^2+(-8x)/2x^2-3+5=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2+3x+(-8x)=0

We get rid of parentheses

4x^2+3x-8x=0

We add all the numbers together, and all the variables

4x^2-5x=0

a = 4; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·4·0
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*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*4}=\frac{10}{8}
=1+1/4
$