I/3x-5+171=x

Solution for I/3x-5+171=x equation:

/3I-5+171=I

We move all terms to the left:

/3I-5+171-(I)=0


Domain of the equation: 3I!=0

I!=0/3

I!=0

I∈R


We add all the numbers together, and all the variables

-1I+/3I+166=0

We multiply all the terms by the denominator


-1I*3I+166*3I+=0

We add all the numbers together, and all the variables

-1I*3I+166*3I=0

Wy multiply elements

-3I^2+498I=0

a = -3; b = 498; c = 0;
Δ = b2-4ac
Δ = 4982-4·(-3)·0
Δ = 248004
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$I_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$I_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{248004}=498$
$I_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(498)-498}{2*-3}=\frac{-996}{-6}
=+166
$
$I_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(498)+498}{2*-3}=\frac{0}{-6}
=0
$