5/x-2=13/2x-3

Solution for 5/x-2=13/2x-3 equation:

5/x-2=13/2x-3

We move all terms to the left:

5/x-2-(13/2x-3)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


10x/2x^2+(-13x)/2x^2+3-2=0

We add all the numbers together, and all the variables

10x/2x^2+(-13x)/2x^2+1=0

We multiply all the terms by the denominator


10x+(-13x)+1*2x^2=0

Wy multiply elements

2x^2+10x+(-13x)=0

We get rid of parentheses

2x^2+10x-13x=0

We add all the numbers together, and all the variables

2x^2-3x=0

a = 2; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·2·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*2}=\frac{6}{4}
=1+1/2
$