7/6x+1/12=3+5/18x

Solution for 7/6x+1/12=3+5/18x equation:

7/6x+1/12=3+5/18x

We move all terms to the left:

7/6x+1/12-(3+5/18x)=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

7/6x-(5/18x+3)+1/12=0

We get rid of parentheses

7/6x-5/18x-3+1/12=0

We calculate fractions


108x^2/1296x^2+1512x/1296x^2+(-360x)/1296x^2-3=0

We multiply all the terms by the denominator


108x^2+1512x+(-360x)-3*1296x^2=0

Wy multiply elements

108x^2-3888x^2+1512x+(-360x)=0

We get rid of parentheses

108x^2-3888x^2+1512x-360x=0

We add all the numbers together, and all the variables

-3780x^2+1152x=0

a = -3780; b = 1152; c = 0;
Δ = b2-4ac
Δ = 11522-4·(-3780)·0
Δ = 1327104
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1327104}=1152$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1152)-1152}{2*-3780}=\frac{-2304}{-7560}
=32/105
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1152)+1152}{2*-3780}=\frac{0}{-7560}
=0
$