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

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

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

We move all terms to the left:

5/6x+7/12-(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

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

We get rid of parentheses

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

We calculate fractions


756x^2/1296x^2+1080x/1296x^2+(-360x)/1296x^2-3=0

We multiply all the terms by the denominator


756x^2+1080x+(-360x)-3*1296x^2=0

Wy multiply elements

756x^2-3888x^2+1080x+(-360x)=0

We get rid of parentheses

756x^2-3888x^2+1080x-360x=0

We add all the numbers together, and all the variables

-3132x^2+720x=0

a = -3132; b = 720; c = 0;
Δ = b2-4ac
Δ = 7202-4·(-3132)·0
Δ = 518400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{518400}=720$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(720)-720}{2*-3132}=\frac{-1440}{-6264}
=20/87
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(720)+720}{2*-3132}=\frac{0}{-6264}
=0
$