4/x=11/5x+13

Solution for 4/x=11/5x+13 equation:

4/x=11/5x+13

We move all terms to the left:

4/x-(11/5x+13)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x+13)!=0

x∈R


We get rid of parentheses

4/x-11/5x-13=0

We calculate fractions


20x/5x^2+(-11x)/5x^2-13=0

We multiply all the terms by the denominator


20x+(-11x)-13*5x^2=0

Wy multiply elements

-65x^2+20x+(-11x)=0

We get rid of parentheses

-65x^2+20x-11x=0

We add all the numbers together, and all the variables

-65x^2+9x=0

a = -65; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-65)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-65}=\frac{-18}{-130}
=9/65
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-65}=\frac{0}{-130}
=0
$