243-12x/18x=x

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Solution for 243-12x/18x=x equation: 



243-12x/18x=x

We move all terms to the left:

243-12x/18x-(x)=0



Domain of the equation: 18x!=0

x!=0/18

x!=0

x∈R



We add all the numbers together, and all the variables

-1x-12x/18x+243=0

We multiply all the terms by the denominator


-1x*18x-12x+243*18x=0

We add all the numbers together, and all the variables

-12x-1x*18x+243*18x=0

Wy multiply elements

-18x^2-12x+4374x=0

We add all the numbers together, and all the variables

-18x^2+4362x=0

a = -18; b = 4362; c = 0;
Δ = b2-4ac
Δ = 43622-4·(-18)·0
Δ = 19027044
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19027044}=4362$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4362)-4362}{2*-18}=\frac{-8724}{-36}
=242+1/3
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4362)+4362}{2*-18}=\frac{0}{-36}
=0
$

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