7/12+1/6x=1/2x

Solution for 7/12+1/6x=1/2x equation:

7/12+1/6x=1/2x

We move all terms to the left:

7/12+1/6x-(1/2x)=0


Domain of the equation: 6x!=0

x!=0/6

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

1/6x-(+1/2x)+7/12=0

We get rid of parentheses

1/6x-1/2x+7/12=0

We calculate fractions


168x^2/144x^2+24x/144x^2+(-72x)/144x^2=0

We multiply all the terms by the denominator


168x^2+24x+(-72x)=0

We get rid of parentheses

168x^2+24x-72x=0

We add all the numbers together, and all the variables

168x^2-48x=0

a = 168; b = -48; c = 0;
Δ = b2-4ac
Δ = -482-4·168·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-48}{2*168}=\frac{0}{336}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+48}{2*168}=\frac{96}{336}
=2/7
$