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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-13)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

10x/2x^2+(-13x)/2x^2+11=0

We multiply all the terms by the denominator


10x+(-13x)+11*2x^2=0

Wy multiply elements

22x^2+10x+(-13x)=0

We get rid of parentheses

22x^2+10x-13x=0

We add all the numbers together, and all the variables

22x^2-3x=0

a = 22; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·22·0
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*22}=\frac{0}{44}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*22}=\frac{6}{44}
=3/22
$