2/3x=5/12x-712

Solution for 2/3x=5/12x-712 equation:

2/3x=5/12x-712

We move all terms to the left:

2/3x-(5/12x-712)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 12x-712)!=0

x∈R


We get rid of parentheses

2/3x-5/12x+712=0

We calculate fractions


24x/36x^2+(-15x)/36x^2+712=0

We multiply all the terms by the denominator


24x+(-15x)+712*36x^2=0

Wy multiply elements

25632x^2+24x+(-15x)=0

We get rid of parentheses

25632x^2+24x-15x=0

We add all the numbers together, and all the variables

25632x^2+9x=0

a = 25632; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·25632·0
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*25632}=\frac{-18}{51264}
=-1/2848
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*25632}=\frac{0}{51264}
=0
$