I/3x=x-22

Solution for I/3x=x-22 equation:

/3I=I-22

We move all terms to the left:

/3I-(I-22)=0


Domain of the equation: 3I!=0

I!=0/3

I!=0

I∈R


We get rid of parentheses

/3I-I+22=0

We multiply all the terms by the denominator


-I*3I+22*3I+=0

We add all the numbers together, and all the variables

-I*3I+22*3I=0

Wy multiply elements

-3I^2+66I=0

a = -3; b = 66; c = 0;
Δ = b2-4ac
Δ = 662-4·(-3)·0
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$I_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$I_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$I_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-66}{2*-3}=\frac{-132}{-6}
=+22
$
$I_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+66}{2*-3}=\frac{0}{-6}
=0
$