5/6x+12=4/3x-6

Solution for 5/6x+12=4/3x-6 equation:

5/6x+12=4/3x-6

We move all terms to the left:

5/6x+12-(4/3x-6)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x-6)!=0

x∈R


We get rid of parentheses

5/6x-4/3x+6+12=0

We calculate fractions


15x/18x^2+(-24x)/18x^2+6+12=0

We add all the numbers together, and all the variables

15x/18x^2+(-24x)/18x^2+18=0

We multiply all the terms by the denominator


15x+(-24x)+18*18x^2=0

Wy multiply elements

324x^2+15x+(-24x)=0

We get rid of parentheses

324x^2+15x-24x=0

We add all the numbers together, and all the variables

324x^2-9x=0

a = 324; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·324·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*324}=\frac{0}{648}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*324}=\frac{18}{648}
=1/36
$