1/3x-8/x=11

Solution for 1/3x-8/x=11 equation:

1/3x-8/x=11

We move all terms to the left:

1/3x-8/x-(11)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

-33x^2+x+(-24x)=0

We get rid of parentheses

-33x^2+x-24x=0

We add all the numbers together, and all the variables

-33x^2-23x=0

a = -33; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·(-33)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-23}{2*-33}=\frac{0}{-66}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*-33}=\frac{46}{-66}
=-23/33
$