5/x=5/3x+11

Solution for 5/x=5/3x+11 equation:

5/x=5/3x+11

We move all terms to the left:

5/x-(5/3x+11)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x+11)!=0

x∈R


We get rid of parentheses

5/x-5/3x-11=0

We calculate fractions


15x/3x^2+(-5x)/3x^2-11=0

We multiply all the terms by the denominator


15x+(-5x)-11*3x^2=0

Wy multiply elements

-33x^2+15x+(-5x)=0

We get rid of parentheses

-33x^2+15x-5x=0

We add all the numbers together, and all the variables

-33x^2+10x=0

a = -33; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-33)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-33}=\frac{-20}{-66}
=10/33
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-33}=\frac{0}{-66}
=0
$