1/6x+7/12=3+1/18x

Solution for 1/6x+7/12=3+1/18x equation:

1/6x+7/12=3+1/18x

We move all terms to the left:

1/6x+7/12-(3+1/18x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 18x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/6x-(1/18x+3)+7/12=0

We get rid of parentheses

1/6x-1/18x-3+7/12=0

We calculate fractions


756x^2/1296x^2+216x/1296x^2+(-72x)/1296x^2-3=0

We multiply all the terms by the denominator


756x^2+216x+(-72x)-3*1296x^2=0

Wy multiply elements

756x^2-3888x^2+216x+(-72x)=0

We get rid of parentheses

756x^2-3888x^2+216x-72x=0

We add all the numbers together, and all the variables

-3132x^2+144x=0

a = -3132; b = 144; c = 0;
Δ = b2-4ac
Δ = 1442-4·(-3132)·0
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-144}{2*-3132}=\frac{-288}{-6264}
=4/87
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+144}{2*-3132}=\frac{0}{-6264}
=0
$