8/x=11/3x+5

Solution for 8/x=11/3x+5 equation:

8/x=11/3x+5

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x+5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


24x/3x^2+(-11x)/3x^2-5=0

We multiply all the terms by the denominator


24x+(-11x)-5*3x^2=0

Wy multiply elements

-15x^2+24x+(-11x)=0

We get rid of parentheses

-15x^2+24x-11x=0

We add all the numbers together, and all the variables

-15x^2+13x=0

a = -15; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-15)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-15}=\frac{-26}{-30}
=13/15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-15}=\frac{0}{-30}
=0
$