3/x-3-1/2x-6=5/6

Solution for 3/x-3-1/2x-6=5/6 equation:

3/x-3-1/2x-6=5/6

We move all terms to the left:

3/x-3-1/2x-6-(5/6)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3/x-1/2x-3-6-(+5/6)=0

We add all the numbers together, and all the variables

3/x-1/2x-9-(+5/6)=0

We get rid of parentheses

3/x-1/2x-9-5/6=0

We calculate fractions


(-20x^2)/72x^2+216x/72x^2+(-36x)/72x^2-9=0

We multiply all the terms by the denominator


(-20x^2)+216x+(-36x)-9*72x^2=0

Wy multiply elements

(-20x^2)-648x^2+216x+(-36x)=0

We get rid of parentheses

-20x^2-648x^2+216x-36x=0

We add all the numbers together, and all the variables

-668x^2+180x=0

a = -668; b = 180; c = 0;
Δ = b2-4ac
Δ = 1802-4·(-668)·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-180}{2*-668}=\frac{-360}{-1336}
=45/167
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+180}{2*-668}=\frac{0}{-1336}
=0
$