492/3x=32-1/6x

Solution for 492/3x=32-1/6x equation:

492/3x=32-1/6x

We move all terms to the left:

492/3x-(32-1/6x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

492/3x-(-1/6x+32)=0

We get rid of parentheses

492/3x+1/6x-32=0

We calculate fractions


2952x/18x^2+3x/18x^2-32=0

We multiply all the terms by the denominator


2952x+3x-32*18x^2=0

We add all the numbers together, and all the variables

2955x-32*18x^2=0

Wy multiply elements

-576x^2+2955x=0

a = -576; b = 2955; c = 0;
Δ = b2-4ac
Δ = 29552-4·(-576)·0
Δ = 8732025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8732025}=2955$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2955)-2955}{2*-576}=\frac{-5910}{-1152}
=5+25/192
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2955)+2955}{2*-576}=\frac{0}{-1152}
=0
$