5x-13/x-3=0

Solution for 5x-13/x-3=0 equation:

5x-13/x-3=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


5x*x-3*x-13=0

We add all the numbers together, and all the variables

-3x+5x*x-13=0

Wy multiply elements

5x^2-3x-13=0

a = 5; b = -3; c = -13;
Δ = b2-4ac
Δ = -32-4·5·(-13)
Δ = 269
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{269}}{2*5}=\frac{3-\sqrt{269}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{269}}{2*5}=\frac{3+\sqrt{269}}{10}
$