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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


6x/2x^2+(-5x)/2x^2-3+4=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


6x+(-5x)+1*2x^2=0

Wy multiply elements

2x^2+6x+(-5x)=0

We get rid of parentheses

2x^2+6x-5x=0

We add all the numbers together, and all the variables

2x^2+x=0

a = 2; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·2·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*2}=\frac{-2}{4}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*2}=\frac{0}{4}
=0
$