8/9x-1/3=1/4x

Solution for 8/9x-1/3=1/4x equation:

8/9x-1/3=1/4x

We move all terms to the left:

8/9x-1/3-(1/4x)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

8/9x-(+1/4x)-1/3=0

We get rid of parentheses

8/9x-1/4x-1/3=0

We calculate fractions


(-144x^2)/324x^2+288x/324x^2+(-81x)/324x^2=0

We multiply all the terms by the denominator


(-144x^2)+288x+(-81x)=0

We get rid of parentheses

-144x^2+288x-81x=0

We add all the numbers together, and all the variables

-144x^2+207x=0

a = -144; b = 207; c = 0;
Δ = b2-4ac
Δ = 2072-4·(-144)·0
Δ = 42849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{42849}=207$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(207)-207}{2*-144}=\frac{-414}{-288}
=1+7/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(207)+207}{2*-144}=\frac{0}{-288}
=0
$