7/6x-1/3x=5/18

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

7/6x-1/3x=5/18

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-270x^2)/324x^2+378x/324x^2+(-108x)/324x^2=0

We multiply all the terms by the denominator


(-270x^2)+378x+(-108x)=0

We get rid of parentheses

-270x^2+378x-108x=0

We add all the numbers together, and all the variables

-270x^2+270x=0

a = -270; b = 270; c = 0;
Δ = b2-4ac
Δ = 2702-4·(-270)·0
Δ = 72900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{72900}=270$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(270)-270}{2*-270}=\frac{-540}{-540}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(270)+270}{2*-270}=\frac{0}{-540}
=0
$