5x-13/x-5=3

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

5x-13/x-5=3

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

5x-13/x-8=0

We multiply all the terms by the denominator


5x*x-8*x-13=0

We add all the numbers together, and all the variables

-8x+5x*x-13=0

Wy multiply elements

5x^2-8x-13=0

a = 5; b = -8; c = -13;
Δ = b2-4ac
Δ = -82-4·5·(-13)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-18}{2*5}=\frac{-10}{10}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+18}{2*5}=\frac{26}{10}
=2+3/5
$