5/6x-1/3=1/18x-40

Solution for 5/6x-1/3=1/18x-40 equation:

5/6x-1/3=1/18x-40

We move all terms to the left:

5/6x-1/3-(1/18x-40)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 18x-40)!=0

x∈R


We get rid of parentheses

5/6x-1/18x+40-1/3=0

We calculate fractions


(-108x^2)/972x^2+810x/972x^2+(-54x)/972x^2+40=0

We multiply all the terms by the denominator


(-108x^2)+810x+(-54x)+40*972x^2=0

Wy multiply elements

(-108x^2)+38880x^2+810x+(-54x)=0

We get rid of parentheses

-108x^2+38880x^2+810x-54x=0

We add all the numbers together, and all the variables

38772x^2+756x=0

a = 38772; b = 756; c = 0;
Δ = b2-4ac
Δ = 7562-4·38772·0
Δ = 571536
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{571536}=756$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(756)-756}{2*38772}=\frac{-1512}{77544}
=-7/359
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(756)+756}{2*38772}=\frac{0}{77544}
=0
$