1/3x-3=12-5/6x

Solution for 1/3x-3=12-5/6x equation:

1/3x-3=12-5/6x

We move all terms to the left:

1/3x-3-(12-5/6x)=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

1/3x-(-5/6x+12)-3=0

We get rid of parentheses

1/3x+5/6x-12-3=0

We calculate fractions


6x/18x^2+15x/18x^2-12-3=0

We add all the numbers together, and all the variables

6x/18x^2+15x/18x^2-15=0

We multiply all the terms by the denominator


6x+15x-15*18x^2=0

We add all the numbers together, and all the variables

21x-15*18x^2=0

Wy multiply elements

-270x^2+21x=0

a = -270; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-270)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*-270}=\frac{-42}{-540}
=7/90
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-270}=\frac{0}{-540}
=0
$