5/6x+7/12=2+1/18x

Solution for 5/6x+7/12=2+1/18x equation:

5/6x+7/12=2+1/18x

We move all terms to the left:

5/6x+7/12-(2+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

5/6x-(1/18x+2)+7/12=0

We get rid of parentheses

5/6x-1/18x-2+7/12=0

We calculate fractions


756x^2/1296x^2+1080x/1296x^2+(-72x)/1296x^2-2=0

We multiply all the terms by the denominator


756x^2+1080x+(-72x)-2*1296x^2=0

Wy multiply elements

756x^2-2592x^2+1080x+(-72x)=0

We get rid of parentheses

756x^2-2592x^2+1080x-72x=0

We add all the numbers together, and all the variables

-1836x^2+1008x=0

a = -1836; b = 1008; c = 0;
Δ = b2-4ac
Δ = 10082-4·(-1836)·0
Δ = 1016064
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1016064}=1008$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1008)-1008}{2*-1836}=\frac{-2016}{-3672}
=28/51
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1008)+1008}{2*-1836}=\frac{0}{-3672}
=0
$