12+2/3x+4+1/6=40+5+1/2x

Solution for 12+2/3x+4+1/6=40+5+1/2x equation:

12+2/3x+4+1/6=40+5+1/2x

We move all terms to the left:

12+2/3x+4+1/6-(40+5+1/2x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(1/2x+45)+12+4+1/6=0

We add all the numbers together, and all the variables

2/3x-(1/2x+45)+16+1/6=0

We get rid of parentheses

2/3x-1/2x-45+16+1/6=0

We calculate fractions


12x^2/216x^2+144x/216x^2+(-108x)/216x^2-45+16=0

We add all the numbers together, and all the variables

12x^2/216x^2+144x/216x^2+(-108x)/216x^2-29=0

We multiply all the terms by the denominator


12x^2+144x+(-108x)-29*216x^2=0

Wy multiply elements

12x^2-6264x^2+144x+(-108x)=0

We get rid of parentheses

12x^2-6264x^2+144x-108x=0

We add all the numbers together, and all the variables

-6252x^2+36x=0

a = -6252; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-6252)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-6252}=\frac{-72}{-12504}
=3/521
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-6252}=\frac{0}{-12504}
=0
$