4+3/x=13/2x

Solution for 4+3/x=13/2x equation:

4+3/x=13/2x

We move all terms to the left:

4+3/x-(13/2x)=0


Domain of the equation: 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

3/x-(+13/2x)+4=0

We get rid of parentheses

3/x-13/2x+4=0

We calculate fractions


6x/2x^2+(-13x)/2x^2+4=0

We multiply all the terms by the denominator


6x+(-13x)+4*2x^2=0

Wy multiply elements

8x^2+6x+(-13x)=0

We get rid of parentheses

8x^2+6x-13x=0

We add all the numbers together, and all the variables

8x^2-7x=0

a = 8; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·8·0
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*8}=\frac{0}{16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*8}=\frac{14}{16}
=7/8
$