2/3x=1/2x+12

Solution for 2/3x=1/2x+12 equation:

2/3x=1/2x+12

We move all terms to the left:

2/3x-(1/2x+12)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x+12)!=0

x∈R


We get rid of parentheses

2/3x-1/2x-12=0

We calculate fractions


4x/6x^2+(-3x)/6x^2-12=0

We multiply all the terms by the denominator


4x+(-3x)-12*6x^2=0

Wy multiply elements

-72x^2+4x+(-3x)=0

We get rid of parentheses

-72x^2+4x-3x=0

We add all the numbers together, and all the variables

-72x^2+x=0

a = -72; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-72)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-72}=\frac{-2}{-144}
=1/72
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-72}=\frac{0}{-144}
=0
$