I/x-x/6=2/3

Solution for I/x-x/6=2/3 equation:

/I-I/6=2/3

We move all terms to the left:

/I-I/6-(2/3)=0


Domain of the equation: I!=0

I∈R


We add all the numbers together, and all the variables

/I-I/6-(+2/3)=0

We get rid of parentheses

/I-I/6-2/3=0

We calculate fractions


(-9I^2)/54I+()/54I+(-72I)/54I=0

We multiply all the terms by the denominator


(-9I^2)+(-72I)+()=0

We add all the numbers together, and all the variables

(-9I^2)+(-72I)=0

We get rid of parentheses

-9I^2-72I=0

a = -9; b = -72; c = 0;
Δ = b2-4ac
Δ = -722-4·(-9)·0
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$I_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$I_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$I_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-72}{2*-9}=\frac{0}{-18}
=0
$
$I_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+72}{2*-9}=\frac{144}{-18}
=-8
$